
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 $\dfrac{{x}^{2}}{{a}^{2}}+ \dfrac{{y}^{2}}{{b}^{2}}=1 (a > b > 0)$ with left and right foci ${F}_{1}$ and ${F}_{2}$, respectively, determine the maximum value of $|B{F}_{2}||A{F}_{2}|$.

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