
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 value of the following expressions:

1. $\dfrac{1}{\sin {10^{\circ}}} - \dfrac{\sqrt{3}}{\cos {10^{\circ}}}$
2. $\dfrac{\sin {50^{\circ}}\left( 1+\sqrt{3}\tan {10^{\circ}} \right)-\cos {20^{\circ}}}{\cos {80^{\circ}}\sqrt{1-\cos {20^{\circ}}}}$

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