
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
Given in \\(\triangle ABC\\), \\(D\\) is a point on side \\(AC\\), \\(BC=2 \sqrt {2}\\), \\(∠DBC=45^{\\circ}\\).  
(Ⅰ) If \\(CD=2 \sqrt {5}\\), find the area of \\(\triangle BCD\\);  
(Ⅱ) If angle \\(C\\) is acute, \\(AB=6 \sqrt {2}\\), \\(\sin A= \dfrac { \sqrt {10}}{10}\\), find the length of \\(CD\\).

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