
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
Suppose there are $n$ pieces stacked in square $h8$ (the top-right corner) on a chessboard. It is allowed to take pieces from the stack one by one and move them either down or left each time, but before reaching square $a1$ (the bottom-left corner), no piece can be stacked on top of another piece. Find the maximum natural number $n$ such that starting from a stack of $n$ pieces in square $h8$, it is possible to have these $n$ pieces stacked in any given order in square $a1$.

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