
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\\), the sides opposite to angles \\(A\\), \\(B\\), and \\(C\\) are \\(a\\), \\(b\\), and \\(c\\) respectively. It is given that \\(a+b=5\\), \\(c=\sqrt{7}\\), and \\(4{{\left( \sin \frac{A+B}{2} \right)}^{2}}-\cos 2C=\frac{7}{2}\\).

    \\((1)\\) Find the magnitude of angle \\(C\\);

    \\((2)\\) Find the area of \\(\triangle ABC\\).

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