
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 curve $C: \frac{x^2}{4} + \frac{y^2}{3} = 1$, and the line $l: \begin{cases} x=1+\frac{1}{2}t \\ y=2+\frac{\sqrt{3}}{2}t \end{cases}$ (where $t$ is a parameter).

(1) Write the parametric equations for curve $C$ and the standard equation for line $l$.

(2) Let $M(1,2)$, and the intersection points of line $l$ with curve $C$ be $A$ and $B$. Find the value of $|MA| \cdot |MB|$.

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