
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 ellipse $\dfrac{{x}^{2}}{4}+\dfrac{{y}^{2}}{3}=1$, a line $l$ passes through its left focus ${F}_{1}$ at an angle of $45{}^\circ$. The line $l$ intersects the ellipse at points $A$ and $B$. Find the length of the line segment $AB$.

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