
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 the terminal side of angle $\theta$ passes through point $P(4a,3a)$ where $(a < 0)$.  
$(1)$ Find the values of $\sin \theta$ and $\cos \theta$;  
$(2)$ Find the value of $\frac{1+2\sin(\pi+\theta)\cos(2023\pi-\theta)}{\sin^{2}(\frac{\pi}{2}+\theta)-\cos^{2}(\frac{5\pi}{2}-\theta)}$.

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