
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
What is the largest positive integer  $n$  less than  $10, 000$  such that in base  $4$ ,  $n$  and  $3n$  have the same number of digits; in base  $8$ ,  $n$  and  $7n$  have the same number of digits; and in base  $16$ ,  $n$  and  $15n$  have the same number of digits? Express your answer in base  $10$ .

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