
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 $\overrightarrow{a}$, $\overrightarrow{b}$, and $\overrightarrow{c}$ satisfy $\overrightarrow{a} \parallel \overrightarrow{b}$ and $\overrightarrow{a} \perp \overrightarrow{c}$, calculate the value of $\overrightarrow{c} \cdot (\overrightarrow{a} + 2\overrightarrow{b})$.

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