
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 equation of line $l$ as $$\begin{cases} x= \sqrt {3}+t\cos\theta \\ y=t\sin\theta \end{cases}(t\text{ is a parameter}, 0\leq\theta<\pi),$$ and the polar equation of curve $C$ as $\rho^2= \frac {4}{1+3\sin^{2}\theta }$  
(1) Write the standard equation of curve $C$;  
(2) If $F_1$ is the left focus of curve $C$, and line $l$ intersects curve $C$ at points $A$ and $B$, find the minimum value of $|F_1A|\cdot|F_1B|$.

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