
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 that F1 and F2 are the two foci of an ellipse $$\frac {x^{2}}{a^{2}} + \frac {y^{2}}{b^{2}} = 1$$, where a > b > 0, P is a point on the ellipse, $$\overrightarrow {PF_{1}} \cdot \overrightarrow {PF_{2}} = 0$. If the area of △PF1F2 is 9, find the value of b.

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