
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 the function $f(x)=ax^{2}+bx-\ln x (a,b \in \mathbb{R})$.
(1) If $b=2-a$, find the number of zeros of $f(x)$.
(2) If $a > 0$, and for any $x > 0$, $f'(1)=0$, determine whether $\ln a+2b$ is necessarily negative, and explain the reason.

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