
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
Given any positive integer, we can write the integer in base 12 and add together the digits of its base 12 representation. We perform this operation on the number \( 7^{6^{5^{3^{2^{1}}}}} \) repeatedly until a single base 12 digit remains. Find this digit.

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