
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

$$
\sqrt{3 x-7}-\sqrt{3 x^{2}-13 x+13} \geqslant 3 x^{2}-16 x+20
$$

In the answer, indicate the sum of all integer values \( x \) that satisfy the inequality.

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