
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
Given $a$, $b$, $c$ be the sides opposite to the internal angles $A$, $B$, $C$ of $\triangle ABC$, and $\frac{a}{b}+\frac{b}{a}=4\cos C$, determine the value of $\frac{\tan C}{\tan A}+\frac{\tan C}{\tan B}$.

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