
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 xOy, the parametric equations of circle C are $$\begin{cases} \left.\begin{matrix}x=5\cos\theta \\ y=5\sin\theta\end{matrix}\right.\end{cases}$$ (where $\theta$ is the parameter), and line l passes through point P(3, 2) with an inclination angle of $$\frac{\pi}{3}$$.  
(Ⅰ) Write the parametric equations of line l and the standard equation of circle C;  
(Ⅱ) Suppose line l intersects circle C at points A and B, determine the value of $|PA| \cdot |PB|$.

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