
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 that vector $\overrightarrow{a}+\overrightarrow{b}=-\overrightarrow{c}$, $\left|\overrightarrow{a}\right|=3$, $\left|\overrightarrow{b}\right|=\left|\overrightarrow{c}\right|=2$, evaluate the expression $\overrightarrow{a}\cdot\overrightarrow{b}+\overrightarrow{b}\cdot\overrightarrow{c}+\overrightarrow{c}\cdot\overrightarrow{a}$.

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