To achieve the desired aggregation of action strings in Presto SQL, you can follow a step-by-step approach that handles variable string lengths and aligns them correctly from the right (most recent day). Below is a comprehensive solution that:

1. **Reverses** each action string to align the days from left to right.
2. **Pads** each reversed string with `'0'` to match the maximum length among all strings.
3. **Splits** the padded strings into individual characters.
4. **Aggregates** the characters by position, prioritizing `'1'` over `'0'`.
5. **Reassembles** the aggregated characters into the final aggregated string and reverses it back to the original order.

### Step-by-Step Solution

Assuming you have a table named `actions` with a column `action_str` that contains the action strings, here's how you can perform the aggregation:

```sql
WITH
  -- Step 1: Reverse each action string to align days from left to right
  reversed AS (
    SELECT
      reverse(action_str) AS reversed_str
    FROM actions
  ),

  -- Step 2: Determine the maximum length among all reversed strings
  max_length AS (
    SELECT
      max(length(reversed_str)) AS max_len
    FROM reversed
  ),

  -- Step 3: Pad each reversed string with '0's to match the maximum length
  padded AS (
    SELECT
      reversed_str || repeat('0', max_length.max_len - length(reversed_str)) AS padded_str
    FROM reversed, max_length
  ),

  -- Step 4: Generate a sequence of positions from 1 to max_len
  positions AS (
    SELECT
      sequence(1, max_length.max_len) AS pos_seq
    FROM max_length
  ),

  -- Step 5: Explode each padded string into individual characters with their positions
  exploded AS (
    SELECT
      pos,
      substr(padded_str, pos, 1) AS char
    FROM padded
    CROSS JOIN UNNEST((SELECT pos_seq FROM positions)) AS t(pos)
  ),

  -- Step 6: Aggregate the characters by position, prioritizing '1' over '0'
  aggregated AS (
    SELECT
      pos,
      max(char) AS max_char
    FROM exploded
    GROUP BY pos
    ORDER BY pos
  )

-- Step 7: Concatenate the aggregated characters and reverse the string back to original order
SELECT
  reverse(array_join(array_agg(max_char ORDER BY pos), '')) AS aggregated_action_str
FROM aggregated;
```

### Explanation of Each Step

1. **Reverse the Strings**: By reversing the strings, the most recent day aligns to the left, making it easier to handle variable lengths.

2. **Determine Maximum Length**: Find the longest string to know how much padding is needed for shorter strings.

3. **Pad the Strings**: Append `'0'` to the end of each reversed string so that all strings have the same length. This ensures proper alignment when aggregating.

4. **Generate Positions**: Create a sequence of numbers representing each position in the string (i.e., each day).

5. **Explode Strings**: Break down each padded string into individual characters along with their respective positions.

6. **Aggregate Characters**: For each position, determine the maximum character (`'1'` if any string has `'1'`, otherwise `'0'`). This prioritizes actions that happened (`'1'`) over those that did not (`'0'`).

7. **Reassemble the Final String**: Concatenate the aggregated characters back into a single string and reverse it to restore the original day order.

### Example

Suppose you have the following `actions` table:

| action_str |
|------------|
| "1010"     |
| "011"      |
| "1"         |

**After Reversing and Padding:**

| reversed_str | padded_str |
|--------------|------------|
| "0101"       | "0101"     |
| "110"        | "1100"     |
| "1"          | "1000"     |

**Aggregated by Position:**

| pos | max_char |
|-----|----------|
| 1   | '1'      |
| 2   | '1'      |
| 3   | '0'      |
| 4   | '1'      |

**Final Aggregated String:**

- Aggregated characters: `'1'`, `'1'`, `'0'`, `'1'`
- Concatenated string: `"1101"`
- Reversed back: `"1011"`

### Final Output

The final output will be a single aggregated string that prioritizes `'1'` over `'0'` for each day, correctly aligned from the most recent day.

```sql
SELECT
  reverse(array_join(array_agg(max_char ORDER BY pos), '')) AS aggregated_action_str
FROM aggregated;
```

This will return:

| aggregated_action_str |
|-----------------------|
| "1011"                |

### Notes

- **Performance Considerations**: For large datasets, ensure that the operations, especially `UNNEST` and `array_agg`, are optimized and consider indexing if necessary.
- **Edge Cases**: Handle cases where some strings might be empty or contain invalid characters by adding appropriate validations.

Feel free to adjust the table and column names as per your actual database schema.