
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
Simplify the following expressions:
(1) $sin \alpha \cdot cos \alpha \cdot (tan \alpha + cot \alpha)$;
(2) $\frac{\sqrt{1 - 2sin\theta cos\theta}}{sin\theta - \sqrt{1 - sin^2\theta}}$, where $\theta \in (0, \frac{\pi}{4})$.

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