
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. Simplify and evaluate the expression: $\log_{\frac{1}{3}} \sqrt{27} + \lg 25 + \lg 4 + 7^{-\log_{7} 2} + (-0.98)^0$
2. Given a point $P(\sqrt{2}, -\sqrt{6})$ on the terminal side of angle $\alpha$, evaluate: $\frac{\cos \left( \frac{\pi}{2} + \alpha \right) \cos \left( 2\pi - \alpha \right) + \sin \left( -\alpha - \frac{\pi}{2} \right) \cos \left( \pi - \alpha \right)}{\sin \left( \pi + \alpha \right) \cos \left( \frac{\pi}{2} - \alpha \right)}$

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