
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 $\cos(\pi - \theta) > 0$, and $\cos\left(\frac{\pi}{2} + \theta\right)(1 - 2\cos^2\left(\frac{\theta}{2}\right)) < 0$, find the value of $\frac{\sin\theta}{|\sin\theta|} + \frac{|\cos\theta|}{\cos\theta} + \frac{\tan\theta}{|\tan\theta|}$.

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