
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 curve C with the polar coordinate equation $ρ \sin^2 θ = 4 \cos θ$, and the lines $l\_1: θ = \frac{π}{3}$ and $l\_2: ρ \sin θ = 4 \sqrt{3}$ intersect with curve C at points A and B respectively (A is not the pole),

1. Find the polar coordinate equations of points A and B;
2. If O is the pole, find the area of triangle AOB.

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