
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 four propositions:

1. If vector $\overrightarrow{a}$ is collinear with $\overrightarrow{b}$, then $\overrightarrow{a} = \overrightarrow{b}$ or $\overrightarrow{a} = -\overrightarrow{b}$;

2. $x \leqslant 3$ is a necessary but not sufficient condition for $|x| \leqslant 3$;

3. Proposition $p$: $\exists x_0 \in (0,2)$, $x_0^2 - 2x_0 - 3 < 0$ and its negation $\neg p$: $\forall x \in (0,2)$, $x^2 - 2x - 3 \geqslant 0$;

4. "The exponential function $y = a^x$ is an increasing function, and $y = \left( \frac{1}{2} \right)^x$ is an exponential function, so $y = \left( \frac{1}{2} \right)^x$ is an increasing function" This syllogism has a false major premise, but the form of reasoning is correct.

The number of correct propositions above is $\boxed{\text{D: }3}$.

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