
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 and find the value of:<br/>$(1)\tan 10^{\circ}\tan 20^{\circ}+\sqrt{3}(\tan10^{\circ}+\tan20^{\circ})$.<br/>$(2)\tan 23^{\circ}+\tan 37^{\circ}+\sqrt{3}\tan 23^{\circ}\tan 37^{\circ}$.

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