
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 the set $\{x \mid a \leq x \leq b\}$, we define $b-a$ as its length. Let sets $A=\{x \mid a \leq x \leq a+1981\}$ and $B=\{x \mid b-1014 \leq x \leq b\}$, where $A$ and $B$ are subsets of $U=\{x \mid 0 \leq x \leq 2012\}$. Find the minimum length of the set $A \cap B$.

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