
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 two vectors such that
\[\|\mathbf{a} + 2\mathbf{b}\| = 2\|\mathbf{a}\|.\]
Find the angle between the vectors \(\mathbf{a} + \mathbf{b}\) and \(\mathbf{b} + 2\mathbf{a}\) in degrees.

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