
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 left and right foci of the ellipse E: x² + $\frac {y^{2}}{b^{2}}$ = 1 (0 < b < 1), respectively. A line passing through point F₁ intersects ellipse E at points A and B. If |AF₁| = 3|BF₁| and AF₂ is perpendicular to the x-axis, find the value of b.

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