
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 \(\mathbf{v}\) be a vector \((a, b)\) in \(\mathbb{R}^2\), and let \(\mathbf{u}(\theta)\) be a unit vector \((\cos\theta, \sin\theta)\). Find the minimum and maximum values of the dot product \(\mathbf{v} \cdot \mathbf{u}(\theta)\) as \(\theta\) varies from 0 to \(2\pi\).

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