
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 vectors $\overrightarrow{a} = (1, -2)$ and $\overrightarrow{b} = (-3, 2)$. If the directed line segments representing vectors $3\overrightarrow{a}$, $2\overrightarrow{b} - \overrightarrow{a}$, and $\overrightarrow{c}$ can be connected head-to-tail to form a triangle, then calculate the value of $\overrightarrow{a} \cdot \overrightarrow{c}$.

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