
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 have a three-digit number in which the digit in the unit's place is the geometric mean of the other two digits. The digit in the ten's place is $\frac{1}{6}$ of the sum of the other digits. If we subtract 396 from this number, the digits of the resulting number appear in reverse order. What is this number?

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