
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 parametric equations of line $l$ as $\begin{cases}x=2+ \frac{ \sqrt{2}}{2}t \\ y= \frac{ \sqrt{2}}{2}t\end{cases} (t \text{ is the parameter})$ and the parametric equations of curve $C$ as $\begin{cases}x=4\cos \;\;\theta \\ y=2 \sqrt{3}\sin \theta\end{cases} (\theta \text{ is the parameter})$, suppose line $l$ intersects curve $C$ at points $A$ and $B$.

(1) Find the ordinary equations of line $l$ and curve $C$;

(2) Let $P(2,0)$, find the value of $|PA| \cdot |PB|$.

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