
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 $|A \cap B|$ as the number of elements in the set $A \cap B$. Given $A=\{a \mid 1 \leqslant a \leqslant 2000, a = 4k + 1, k \in \mathbf{Z}\}$ and $B = \{b \mid 1 \leqslant b \leqslant 3000, b = 3k - 1, k \in \mathbf{Z}\}$, find $|A \cap B|$.

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