
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 $$C: \frac {x^{2}}{4}+ \frac {y^{2}}{b^{2}}=1(0＜b＜2)$$, a straight line with a slope angle of $$\frac {3π}{4}$$ intersects the ellipse C at points A and B. The midpoint of the line segment AB is M, and O is the coordinate origin. The angle between $$\overrightarrow {OM}$$ and $$\overrightarrow {MA}$$ is θ, and |tanθ|=3. Find the value of b.

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