
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
Suppose that a planet contains  $\left(CCAMATHBONANZA_{71}\right)^{100}$  people ( $100$  in decimal), where in base  $71$  the digits  $A,B,C,\ldots,Z$  represent the decimal numbers  $10,11,12,\ldots,35$ , respectively. Suppose that one person on this planet is snapping, and each time they snap, at least half of the current population disappears. Estimate the largest number of times that this person can snap without disappearing. An estimate of  $E$  earns  $2^{1-\frac{1}{200}\left|A-E\right|}$  points, where  $A$  is the actual answer.

*2019 CCA Math Bonanza Lightning Round #5.2*

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