
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 $f(x) = 6\ln x - ax^2 - 7x + b$ (where $a$ and $b$ are constants), and $x=2$ is an extremum point of $f(x)$.
1. Find $a$.
2. Determine the intervals of monotonicity for the function $f(x)$.
3. If the graph of $y=f(x)$ intersects the x-axis at exactly three distinct points, find the range of values for $b$. (Given $\ln2=0.693$, $\ln1.5=0.405$)

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