
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Pat and Mat were practicing calculations. In a square grid oriented according to the cardinal directions, they assigned the following mathematical operations for moving one square:

- For a move to the North (N), they added seven.
- For a move to the East (E), they subtracted four.
- For a move to the South (S), they divided by two.
- For a move to the West (W), they multiplied by three.

For example, when Mat gave Pat the number 5 and the path N-E-S, they correctly calculated the result to be 4.

What number did Pat give Mat if, for the path N-E-S-W-W-S-E-N, the correct calculation result was 57?

Present the answer in LaTex format: \boxed{Your answer}
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