
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 $\{ a_{n}\}$, it satisfies $\overrightarrow{OP}={a}_{2}\overrightarrow{O{P}_{1}}+{a}_{15}\overrightarrow{O{P}_{2}}$, where points $P_{1}$, $P$, and $P_{2}$ are collinear. Find the sum of the first 16 terms of the sequence, denoted as ${S}_{16}=$$\_\_\_\_\_\_．

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