
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 $\triangle ABC$, $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$ respectively.

(1) If $A$, $B$, and $C$ form an arithmetic sequence, find the range of values for $\cos A + \cos C$;  
(2) If $a$, $b$, and $c$ form a geometric sequence, and $\cos B = \frac{4}{5}$, find the value of $\frac{1}{\tan A} + \frac{1}{\tan C}$.

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