
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
The Heron's formula is a formula for calculating the area of a triangle using the lengths of its three sides. It is represented by the formula: $S=\sqrt{p(p-a)(p-b)(p-c)}$ (where $a$, $b$, $c$ are the lengths of the three sides of the triangle, $p=\frac{a+b+c}{2}$, and $S$ is the area of the triangle). Solve the following problem using the above information: When $a=2$, $b=3$, $c=4$.  
$(1)$ Write down the simplified result of $p$ directly as ______.  
$(2)$ Write down the process of calculating the value of $S$.

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