
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
Evaluate or simplify:

1. Evaluate: $\sin ^{2}120^{\circ}+\cos 180^{\circ}+\tan 45^{\circ}-\cos ^{2}(-330^{\circ})+\sin (-210^{\circ})$
2. Simplify the expression given that $\alpha$ is an angle in the third quadrant: $\sqrt{\frac{1+\sin \alpha}{1-\sin \alpha}} - \sqrt{\frac{1-\sin \alpha}{1+\sin \alpha}}$

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