
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 vectors such that $\|\mathbf{p}\| = 2$, $\|\mathbf{q}\| = 3$, $\|\mathbf{r}\| = 4$, and
\[\mathbf{p} \times (\mathbf{p} \times \mathbf{r}) + \mathbf{q} = 2\mathbf{q}.\]
Find the smallest possible angle between $\mathbf{p}$ and $\mathbf{r}$, in degrees.

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