
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 a line $l$ that passes through point $P(2,0)$ and intersects the parabola $T$: $y^{2}{=}4x$ at points $A$ and $B$, and intersects the $y$-axis at point $C$. Point $A$ is located in the fourth quadrant and $O$ is the origin.

(1) When $A$ is the midpoint of $PC$, find the equation of line $l$;

(2) A circle with $AB$ as its diameter intersects line $OB$ at point $D$. Find $|OB|·|OD|$.

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