
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 equation of the ellipse is $\frac{x^2}{4}+\frac{y^2}{3}=1$, $F_1$ and $F_2$ are the left and right foci of the ellipse, respectively. The chord $PQ$ passes through the right focus $F_2$ of the ellipse. The maximum area of $\Delta PF_1Q$ is \_\_\_\_

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