
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 values of the following expressions:
1. $\cos ^{2}15^{\circ}-\sin ^{2}15^{\circ}$;
2. $\frac{{1+\tan15°}}{{1-\tan15°}}$;
3. ${\sin^2}10°+{\cos^2}55°+\sqrt{2}\sin10°\cos55°$.

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