
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 $\sin x=\dfrac{4}{5}$, where $\dfrac{\pi}{2}\leqslant x\leqslant \pi$.

(1) Find the value of $\cos x$,

(2) Find the value of $\dfrac{\cos (-x)}{\sin (\dfrac{\pi }{2}-x)-\sin (2\pi -x)}$.

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