
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 an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\left(a \gt b \gt 0\right)$ with foci $F_{1}$ and $F_{2}$, points $A$ and $B$ on the ellipse, $AB\bot F_{1}F_{2}$ at $F_{2}$, $|AB|=4$, and $|F_{1}F_{2}|=2\sqrt{3}$, find the length of the major axis of the ellipse.

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