
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) = sin(2x - π/6) + 2cos²x,
(I) Find the range of the function f(x) when x ∈ [0, π/2];
(II) In triangle ABC, angles A, B, C correspond to sides a, b, c respectively. If f(A) = 3/2, √2a = √3b, and c = 1 + √3, find the area of triangle ABC.

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