
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
12. Let \([x]\) denote the floor function of \(x\) (i.e., the greatest integer less than or equal to \(x\)). Solve the system of equations:

$$
\left\{\begin{array}{c}
[x+y-3]=2-x \\
[x+1]+[y-7]+x=y
\end{array}\right.
$$

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