
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 smallest positive odd integer n such that 3^(1/7) * 3^(3/7) * ... * 3^((2n+1)/7) is greater than 5000?

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