
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 curve C in the Cartesian coordinate system xOy with the parametric equations $$\begin{cases} x=1+4\cos\theta \\ y=2+4\sin\theta \end{cases}$$ (where $\theta$ is the parameter), and a line l passing through the fixed point P(3, 5) with an inclination angle of $\frac{\pi}{3}$.
(1) Write the parametric equation of the line l and the standard equation of curve C.
(2) Assume the line l intersects curve C at points A and B. Find the value of $|PA| \cdot |PB|$.

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