
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 Chinese mathematician Qin Jiushao of the Southern Song Dynasty proposed the Qin Jiushao formula, also known as the Suanjing Shu formula, which uses the three sides of a triangle to calculate its area. That is, if the three sides of a triangle are $a$, $b$, and $c$, then the area of the triangle is $S=$____. Given that the three sides of triangle $\triangle ABC$ are $2$, $3$, $\sqrt{13}$, the area of $\triangle ABC$ is ____.

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