
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 \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) be unit vectors such that
\[\mathbf{a} \times (\mathbf{b} \times \mathbf{c}) = \frac{2\mathbf{b} + 3\mathbf{c}}{\sqrt{13}},\]
and such that \{\mathbf{a}, \mathbf{b}, \mathbf{c}\} is a linearly independent set.

Find the angle between \(\mathbf{a}\) and \(\mathbf{b}\), in degrees.

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