
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 in integers:

$$
\frac{1}{\sqrt{x-2y+z+1}} + \frac{2}{\sqrt{2x-y+3z-1}} + \frac{3}{\sqrt{3y-3x-4z+3}} > x^2 - 4x + 3
$$

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