
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
Calculate the following expressions:
1. $\cos 263^\circ \cos 203^\circ + \sin 83^\circ \sin 23^\circ$;
2. $\frac{\cos 7^\circ - \sin 15^\circ \sin 8^\circ}{\cos 8^\circ}$.

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