
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 $A$, $B$, $C$ are respectively $a$, $b$, $c$, and it is given that $c\cdot\cos A + a\cdot\cos C = 2b\cdot\cos A$.  
(I) Find $\cos A$;  
(II) If $a= \sqrt{7}$ and $b+c=4$, find the area of $\triangle ABC$.

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