
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
Let $\mathbf{p},$ $\mathbf{q},$ and $\mathbf{r}$ be unit vectors such that
\[\mathbf{p} + 2\mathbf{q} + 2\mathbf{r} = \mathbf{0}.\]Determine the angle between $\mathbf{p}$ and $\mathbf{q},$ in degrees.

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