
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 \( \{x \mid a \leqslant x \leqslant b\} \), we define \( b-a \) as its length. Let the set \( A=\{x \mid a \leqslant x \leqslant a+1981\} \), \( B=\{x \mid b-1014 \leqslant x \leqslant b\} \), and both \( A \) and \( B \) are subsets of the set \( U=\{x \mid 0 \leqslant x \leqslant 2012\} \). The minimum length of the set \( A \cap B \) is ______.

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