
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
(1) Given $\frac{\pi}{2} < a < \pi$, and $\sin(\pi - a) = \frac{4}{5}$, find the value of $\frac{\sin(2\pi + a)\tan(\pi - a)\cos(-\pi - a)}{\sin(\frac{3\pi}{2} - a)\cos(\frac{\pi}{2} + a)}$.  
(2) Given a point P$(\cos\theta, \sin\theta)$ is on the line $y = -2x$, find the value of $\frac{1 + \sin2\theta - \cos2\theta}{1 + \sin2\theta + \cos2\theta}$.

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