
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) = $\overrightarrow{a} \cdot \overrightarrow{b}$, where $\overrightarrow{a}$ = (2cosx, $\sqrt{3}$sin2x) and $\overrightarrow{b}$ = (cosx, 1), x ∈ R.
1. Find the smallest positive period and the monotonically increasing interval of the function y = f(x).
2. In △ABC, the sides a, b, c correspond to angles A, B, C respectively, with f(A) = 2, a = $\sqrt{7}$, and sinB = 2sinC. Find the area of △ABC.

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