
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 $\triangle ABC$, $bcosA+\frac{1}{2}a=c$.  
$(Ⅰ)$ Find the value of angle $B$;  
$(Ⅱ)$ If $c=5$, ____. Find the value of $a$ and calculate the area of $\triangle ABC$;  
Choose one of the conditions from $b=7$ or $C=\frac{π}{4}$, supplement it to the above question, and answer it.

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