
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 famous mathematician Qin Jiushao of the Southern Song Dynasty in China once proposed the "Qin Jiushao Formula" for calculating the area of a triangle using the lengths of its three sides: If the three sides of a triangle are $a$, $b$, and $c$, then the area of the triangle is given by $S=\sqrt{\frac{1}{4}[a^{2}b^{2}-(\frac{a^{2}+b^{2}-c^{2}}{2})^{2}]}$. According to the formula mentioned above, if the three sides of a triangle are $5$, $6$, and $7$, then the area of this triangle is ______.

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