
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, and \\(a+b+c=8\\).  
\\((\\)I\\()\\) If \\(a=2\\) and \\(b= \dfrac {5}{2}\\), find the value of \\(\cos C\\);  
\\((\\)II\\()\\) If \\(\sin A\cos ^{2} \dfrac {B}{2}+\sin B\cos ^{2} \dfrac {A}{2}=2\sin C\\) and the area of \\(\triangle ABC\\), \\(S= \dfrac {9}{2}\sin C\\), find the values of \\(a\\) and \\(b\\).

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