
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
On the square $h8$ of a chessboard, there is a stack of $n$ different checkers. Checkers are allowed to be moved from the stack one square down or to the left. However, it is forbidden to place one checker on top of another on any square except for square $a1$. What is the maximum value of $n$ for which it is possible to obtain any stack on square $a1$ from the initial stack on square $h8$ (considering the order of checkers in the stack)?

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