
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 vectors in space where $\|\mathbf{a}\| = 5$ and $\|\mathbf{b}\| = 2$. If the angle between $\mathbf{a}$ and $\mathbf{b}$ is $\frac{\pi}{3}$, find the value of $(\mathbf{a} + 2\mathbf{b}) \cdot (\mathbf{a} - 2\mathbf{b}).$

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