
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
In a regular octagon $A_1A_2A_3\cdots A_7A_8$ centered at the origin, let $\overrightarrow{a_{0}}=\overrightarrow{A_{8}A_{1}}, \ \vec{a}_{i}=\overrightarrow{A_{i}A_{i+1}} \ (i=1,2,\cdots,7)$, and $\vec{b}_{j}=\overrightarrow{O A_{j}} \ (j=1,2,\cdots,8)$. Find the value of $\vec{a}_{2}+\vec{a}_{5}+\overrightarrow{b_{2}}+\vec{b}_{5}+\vec{b}_{7}$.

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