
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 non-zero vectors $\overrightarrow {a}$, $\overrightarrow {b}$, $\overrightarrow {c}$ that satisfy $\overrightarrow {a}$ + $\overrightarrow {b}$ + $\overrightarrow {c}$ = 0, the angle between vectors $\overrightarrow {a}$ and $\overrightarrow {b}$ is 120°, and $|\overrightarrow {b}| = 2|\overrightarrow {a}|$, find the angle between vectors $\overrightarrow {a}$ and $\overrightarrow {c}$.

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