
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, C are a, b, c, respectively. Given vectors m=(-1,1) and n=(cosB cosC, sinB sinC - √3/2), and m is perpendicular to n.
(1) Find the measure of angle A;
(2) Now, from the following three conditions: ①a=1; ②2c-(√3+1)b=0; ③B=45°, choose two conditions to determine triangle ABC and find the area of the determined triangle ABC.

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