
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 $\mathbf{p},$ $\mathbf{q},$ $\mathbf{r}$ be unit vectors such that 
\[\mathbf{p} \times (\mathbf{q} \times \mathbf{r}) = \frac{\mathbf{q} + 2\mathbf{r}}{2},\] and such that $\{\mathbf{p}, \mathbf{q}, \mathbf{r}\}$ is a linearly independent set. 
Find the angle between $\mathbf{p}$ and $\mathbf{r}$ in degrees.

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