
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 the function f(x) = sinxcos(x - π/6) + 1/2 cos2x.

1. Find the maximum value of the function f(x).
2. Given that the area of △ABC is 4√3, and the sides a, b, and c are opposite to angles A, B, and C respectively. If f(A) = 1/2, b + c = 10, find the value of a.

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