
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
Kevin the Koala eats  $1$  leaf on the first day of its life,  $3$  leaves on the second,  $5$  on the third, and in general eats  $2n-1$  leaves on the  $n$ th day. What is the smallest positive integer  $n>1$  such that the total number of leaves Kevin has eaten his entire  $n$ -day life is a perfect sixth power?

*2015 CCA Math Bonanza Individual Round #4*

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