
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
Evaluate the expression $3^{3^{3^3}}$ according to the standard convention, and if the order in which the exponentiations are performed is changed, find the number of other distinct values that can be obtained.

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