
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 that \(\tan \alpha + \cot \alpha = 4\), find \(\sqrt{\sec^2 \alpha + \csc^2 \alpha - \frac{1}{2} \sec \alpha \csc \alpha}\).

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