
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
Find all integer values of \(a\), not exceeding 15 in absolute value, for which the inequality

$$
\frac{4x - a - 4}{6x + a - 12} \leq 0
$$

holds for all \(x\) in the interval \([2, 3]\). In the answer, indicate the sum of all such \(a\).

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