
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 \( a > 0 \),
\[
f(x) = \ln(2x + 1) + 2ax - 4a e^x + 4.
\]

(1) When \( a = 1 \), find the maximum value of \( f(x) \);

(2) Determine the number of zeros of the function \( f(x) \) and provide a justification.

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