
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 $\overrightarrow{a}+ \overrightarrow{b}+ \overrightarrow{c}= \overrightarrow{0}$, the angle between $\overrightarrow{a}$ and $\overrightarrow{c}$ is $60^{\circ}$, and $|\overrightarrow{b}|= \sqrt {3}|\overrightarrow{a}|$, find the value of $\cos < \overrightarrow{a},\overrightarrow{b} >$.

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