
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
Ankit, Box, and Clark are taking the tiebreakers for the geometry round, consisting of three problems. Problem  $k$  takes each  $k$  minutes to solve. If for any given problem there is a  $\frac13$  chance for each contestant to solve that problem first, what is the probability that Ankit solves a problem first?

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