
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 \(\mathbf{a}\) and \(\mathbf{b}\) be unit vectors such that \(\mathbf{a} + 3 \mathbf{b}\) and \(7 \mathbf{a} - 6 \mathbf{b}\) are orthogonal. Find the angle between \(\mathbf{a}\) and \(\mathbf{b}\), in degrees.

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