
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
Given the sets \( P = \left\{(x, y) \mid y = 2x^2 + 3x + 1, -2 \leq x \leq 3 \right\} \) and \( Q = \{(x, y) \mid x = a, a \in \mathbf{R} \} \), determine the number of elements contained in the set \( P \cap Q \).

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