
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

Find all values of the real parameter \( p \) for which the following system of equations is solvable:

\[ 
\left\{\begin{aligned}
2[x] + y & = \frac{3}{2} \\
3[x] - 2y & = p
\end{aligned}\right.
\]

Here, \([a]\) denotes the integer part of the number \( a \).

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