
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
Among the following propositions:

(1) For line $a,b$ and plane $\alpha$, if $a\parallel b$ and $b\subset \alpha$, then $a\parallel \alpha$.

(2) For lines $a,b$ and planes $\alpha, \beta$, if $a\subset \alpha$, $b\subset \beta$, and $\alpha \perp \beta$, then $a\perp b$.

(3) Cutting a cone with a plane results in a cone and a frustum.

(4) The axial section of a cone is the section through the apex of the cone with the largest area among all sections.

The number of true propositions is ______.

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