
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 an arithmetic sequence $\left\{ a_n \right\}$ with a common difference not equal to $0$, the first term $a_1=3$, and $a_1$, $a_4$, $a_{13}$ form a geometric sequence, find the general formula for the sequence $\left\{ a_n \right\}$, which is $a_n=$_______.

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