
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 $\sin\theta$ and $\cos\theta$ are the two roots of the equation $x^2 - ax + a = 0$ with $a \in \mathbb{R}$,

(1) Find the value of $\cos\left(\frac{\pi}{2} + \theta\right) + \sin\left(\frac{3\pi}{2} + \theta\right)$;
(2) Find the value of $\tan(\pi - \theta) - \frac{1}{\tan\theta}$.

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