
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
In triangle $ABC$, the three internal angles are $A$, $B$, and $C$, and the corresponding three sides are $a$, $b$, and $c$. Given that $\frac{c}{b} + \frac{b}{c} = \frac{5\cos A}{2}$, find the value of $\frac{\tan A}{\tan B} + \frac{\tan A}{\tan C}$ = $\_\_\_\_\_\_\_$.

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