
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
Compute the value of the following expressions:

(1) $\frac{\tan 53^{\circ} + \tan 7^{\circ} + \tan 120^{\circ}}{\tan 53^{\circ} \cdot \tan 7^{\circ}}$;

(2) $\left[2\sin 50^{\circ} + \sin 10^{\circ}(1 + \sqrt{3}\tan 10^{\circ})\right]\sqrt{1 - \cos 160^{\circ}}$.

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