
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
Jacob and Aaron are playing a game in which Aaron is trying to guess the outcome of an unfair coin which shows heads  $\tfrac{2}{3}$  of the time.  Aaron randomly guesses ``heads''  $\tfrac{2}{3}$  of the time, and guesses ``tails'' the other  $\tfrac{1}{3}$  of the time.  If the probability that Aaron guesses correctly is  $p$ , compute  $9000p$ .

*Proposed by Aaron Lin*

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