
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 \( x \) and \( y \) for which
\[
\begin{cases}
  x - 2y + [x] + 3\{x\} - \{y\} + 3[y] = 2.5 \\
  2x + y - [x] + 2\{x\} + 3\{y\} - 4[y] = 12
\end{cases}
\]
where \( [x] \) and \( [y] \) are the integer parts and \( \{x\} \) and \( \{y\} \) are the fractional parts of \( x \) and \( y \) respectively. The integer part of a number \( a \) is the greatest integer less than or equal to \( a \), and \( \{a\} = a - [a] \).

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