
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) $\dfrac{\tan 10^{\circ} \tan 70^{\circ}}{\tan 70^{\circ} - \tan 10^{\circ} + \tan 120^{\circ}}$

(2) $\dfrac{2\cos 40^{\circ} + \cos 10^{\circ}(1 + \sqrt{3}\tan 10^{\circ})}{\sqrt{1 + \cos 10^{\circ}}}$

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