
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 equations

$$
\begin{cases}
2\left[x_{1}\right] + x_{2} & = \frac{3}{2} \\
3\left[x_{1}\right] - 2 x_{2} & = 4
\end{cases}
$$

Here, $[a]$ denotes the integer part of the number $a$.

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