
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 inequality $|x+a| < b$ with respect to $x$, the solution set is $\{x|2 < x < 4\}$.
(1) Find the values of real numbers $a$ and $b$;
(2) Find the maximum value of $\sqrt{at+12}+\sqrt{3bt}$.

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