
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 $a \in \mathbb{R}$, the function $f(x) = \log_{2}\left(\frac{1}{x} + a\right)$.

(1) If $f(1) < 2$, find the range of the real number $a$.

(2) Let the function $g(x) = f(x) - \log_{2}[(a-4)x + 2a - 5]$, discuss the number of zeros of the function $g(x)$.

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