
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 $i$ is the imaginary unit, $(1+2i)z_1 = -1+3i$, $z_2 = 1+(1+i)^{10}$, and the points corresponding to $z_1$ and $z_2$ in the complex plane are $A$ and $B$ respectively, with $O$ being the origin. Calculate the value of $\overrightarrow{OA} \cdot \overrightarrow{OB}$.

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