
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
For real numbers $a$ and $b$, define an operation $a \otimes b = n$ (where $n$ is a constant) that has the properties $(a+1) \otimes b = n+1$ and $a \otimes (b+1) = n-2$. If $1 \otimes 1 = 2$, find the value of $2011 \otimes 2011$.

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