
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
At Stanford in 1988, human calculator Shakuntala Devi was asked to compute  $m = \sqrt[3]{61{,}629{,}875}$  and  $n = \sqrt[7]{170{,}859{,}375}$ .  Given that  $m$  and  $n$  are both integers, compute  $100m+n$ .

*Proposed by Evan Chen*

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