
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) Evaluate: $\frac{\sin 65^{\circ}+\sin 15^{\circ} \sin 10^{\circ}}{\sin 25^{\circ}-\cos 15^{\circ} \cos 80^{\circ}}$
(2) Given $\sin \theta+2 \cos \theta=0$, find the value of $\frac{\cos 2 \theta-\sin 2 \theta}{1+\cos ^{2} \theta}$.

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