
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 $a_0$ be a unit vector. (1) If $a$ is a certain vector in the plane, then $a = |a| \cdot a_0$; (2) If $a$ is parallel to $a_0$, then $a = |a| \cdot a_0$; (3) If $a$ is parallel to $a_0$ and $|a| = 1$, then $a = a_0$. Among these statements, the number of false statements is ______.

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