
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 system of inequalities and write down the smallest integer solution of the system.

\[
\left\{
\begin{array}{l}
5x+7 > 3(x+1) \quad (1) \\
1-\frac{3}{2}x \leq \frac{1}{2}x-1 \quad (2)
\end{array}
\right.
\]

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