
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
Move the pieces. Divide a sheet of paper into 6 squares and place a stack of 15 pieces numbered $1,2,3, \ldots, 15$, from top to bottom, in square $A$. The puzzle is to move the entire stack to square $F$ in the fewest possible moves. You can move one piece at a time to any square, but a larger number cannot be placed on top of a smaller number.

For example, if you place piece 1 in square $B$ and piece 2 in square $C$, you can then place piece 1 on top of piece 2, but not piece 2 on top of piece 1.

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