
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
Define: Use $\{m\}$ to represent the smallest integer greater than $m$, for example, $\{2.5\}=3$, $\{5\}=6$, $\{-1.3\}=-1$, etc.; Use $[m]$ to represent the largest integer not greater than $m$, for example, $[3.2]=3$, $[4]=4$, $[-1.5\]=-2$. If the integers $x$, $y$ satisfy the equation: $3[x]+2\{y\}=2003$, $2\{x\}-[y\]=2001$, then $x+y=$ ?

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