
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
Let ellipse $C$ be $\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{3}=1(a>\sqrt{3})$, with left and right foci $F_{1}$ and $F_{2}$ respectively. If point $A(1,\frac{3}{2})$ lies on $C$, then the perimeter of $\triangle AF_{1}F_{2}$ is ______.

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