
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 $C_{1}$: $\frac{x^2}{a^2}+y^{2}=1\left(a \gt 1\right)$, $C_{2}$: $\frac{x^2}{4}+y^{2}=1$ have eccentricities $e_{1}$, $e_{2}$, respectively. If $e_{2}=\sqrt{3}e_{1}$, calculate the value of $a$.

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