
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
In \\(\triangle ABC\\), \\(a\\), \\(b\\), and \\(c\\) are the sides opposite to angles \\(A\\), \\(B\\), and \\(C\\) respectively, and it is given that \\(2ab\sin C= \sqrt {3}(b^{2}+c^{2}-a^{2})\\). If \\(a= \sqrt {13}\\) and \\(c=3\\), then the area of \\(\triangle ABC\\) is \_\_\_\_\_\_.

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