
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 \\(c= \sqrt{7}\\) and \\(C= \frac{\pi}{3}\\).

(Ⅰ) If \\(2\sin A=3\sin B\\), find \\(a\\) and \\(b\\).

(Ⅱ) If \\(\cos B= \frac{5\sqrt{7}}{14}\\), find \\(\sin 2A\\).

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