
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 vectors $\mathbf{p}$ and $\mathbf{q}$ such that $\|\mathbf{p}\| = 7,$ $\|\mathbf{q}\| = 10,$ and $\|\mathbf{p} + \mathbf{q}\| = 13.$ Find $\cos \phi,$ where $\phi$ is the angle between $\mathbf{p}$ and $\mathbf{q}.$

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