
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
The sum of the first $n$ terms of an arithmetic sequence $a_n$ is denoted as $S_n$. Three different points $A$, $B$, $C$ lie on a line $l$, and point $O$ is off the line $l$. It satisfies the relation $\overrightarrow {OA} = a_2 \overrightarrow {OB} + (a_7 + a_{12}) \overrightarrow {OC}$. Find the value of $S_{13}$.

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