
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
Determine the largest integer  $n$  such that  $2^n$  divides the decimal representation given by some permutation of the digits  $2$ ,  $0$ ,  $1$ , and  $5$ . (For example,  $2^1$  divides  $2150$ . It may start with  $0$ .)

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