
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
Simplify the following expressions:

(1) $\sin^{4}{\alpha} + \tan^{2}{\alpha} \cdot \cos^{4}{\alpha} + \cos^{2}{\alpha}$

(2) $\frac{\cos{(180^{\circ} + \alpha)} \cdot \sin{(\alpha + 360^{\circ})}}{\sin{(-\alpha - 180^{\circ})} \cdot \cos{(-180^{\circ} - \alpha)}}$

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