
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
In the Cartesian coordinate system, line $l$ passes through point $P(3,0)$ with an inclination angle $α = \frac{\pi}{4}$.
1. Write the parametric equations for line $l$.
2. With the origin as the pole and the positive half of the x-axis as the polar axis, establish a polar coordinate system. Given the curve $C: \rho = 4\cos\theta$ intersects with line $l$ at two points $A$ and $B$, find the coordinates of the midpoint of $AB$ and the product of the distances from point $P$ to points $A$ and $B$.

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