
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 following inequalities (set):

(1) $3(2x+2) > 4x-1+7$; (2) Solve the system of inequalities $\begin{cases}x+1 > 0, \\ x\leqslant \frac{x-2}{3}+2,\end{cases}$ and list all the integer solutions that satisfy this system of inequalities.

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