
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 proposition p: For all $x, y \in \mathbb{N}$, point $P(x, y)$ is in the first quadrant; proposition q: There exists an $x \in \mathbb{R}$, such that $x^2 - 5x + 6 = 0$ holds. Then, among the propositions "p or q", "p and q", "not p or not q", and "not p and q", the number of true propositions is ____.

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