
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 that \( a \) and \( b \) are real numbers, and the following system of inequalities in terms of \( x \):
\[
\left\{\begin{array}{l}
20x + a > 0, \\
15x - b \leq 0
\end{array}\right.
\]
has integer solutions of only 2, 3, and 4, find the maximum value of \( ab \).

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