
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
Ancient Chinese mathematician Qin Jiushao described the "method of three obliques for finding the area," which is to find the area of a triangle when the lengths of its three sides are known. It can be represented by the formula: $S=\sqrt{\frac{1}{4}[{{a^2}{b^2}-{{({\frac{{{a^2}+{b^2}-{c^2}}}{2}})}^2}}]}$ (where $a$, $b$, $c$ are the lengths of the triangle's three sides, and $S$ is the area). Then, the area of a triangle with $a=\sqrt{5}$, $b=3$, $c=2\sqrt{3}$ is ____.

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