
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 $f\left( x \right)=\frac{3}{2}{{x}^{2}}-2ax (a > 0)$ and $g\left( x \right)={{a}^{2}}\ln x+b$, they share a common point, and their tangent lines at the common point are identical. The maximum value of the real number $b$ is ___.

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