
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 $\triangle ABC$, $a$, $b$, $c$ are the lengths of the sides opposite to angles $A$, $B$, $C$ respectively, and $b^{2}+c^{2}-a^{2}=bc$.<br/>$(Ⅰ)$ Given ________, calculate the area of $\triangle ABC$;<br/>Choose any two of the conditions from ① $a=\sqrt{7}$, ② $b=2$, ③ $\sin C=2\sin B$ to complete the question $(Ⅰ)$ and answer it.<br/>$(Ⅱ)$ Find the maximum value of $\cos B+\cos C$.

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