
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
Solve the inequality:
$$
9 \cdot \frac{|x+4|-|x-2|}{|3x+14|-|3x-8|} + 11 \cdot \frac{|x+4|+|x-2|}{|3x+14|+|3x-8|} \leqslant 6
$$

In the answer, write down the sum of its integer solutions that satisfy the condition $|x|<110$.

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