
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
Let set \(A = \left\{ n \mid \frac{n}{3} \in \mathbf{N}_{+} \right\}\), and
\[ B = \left\{ y \mid y = x + 4 + \sqrt{5 - x^2} \right\}. \]
Determine the number of elements in the set \( A \cap B \).

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