
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
Given that $1^2 + 2^2 = \frac{2 \times 3 \times 5}{6}$, $1^2 + 2^2 + 3^2 = \frac{3 \times 4 \times 7}{6}$, and $1^2 + 2^2 + 3^2 + 4^2 = \frac{4 \times 5 \times 9}{6}$, ..., determine the value of $n$ if $1^2 + 2^2 + 3^2 + 4^2 + \dots + n^2 = 385$.

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