
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
We place a mouse in one corner cube of a $3 \times 3 \times 3$ grid and a piece of cheese in the central cube. The mouse wanders randomly in search of the cheese: in each move, it randomly steps into one of the neighboring cubes. On average, how many steps will it take for the mouse to find the cheese?

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