
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
An arithmetic sequence $\{ a_n \}$ has the first term equal to $1$ and a non-zero common difference. If $a_{2}, a_{3}, a_{6}$ form a geometric sequence, what is the sum of the first $6$ terms of $\{ a_n \}$?

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