
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
Given the vectors \(\boldsymbol{m}=(\cos x, -\sin x)\) and \(\boldsymbol{n}=(\cos x, \sin x - 2 \sqrt{3} \cos x)\), \(x \in \mathbf{R}\), determine the range of \(f(x) = \boldsymbol{m} \cdot \boldsymbol{n}\) for \(x \in \left[\frac{\pi}{4}, \frac{\pi}{2}\right]\).

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