
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 $$C: \frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1(a>b>0)$$ with its left and right foci being F<sub>1</sub> and F<sub>2</sub>, and its top vertex being B. If the perimeter of $\triangle BF_{1}F_{2}$ is 6, and the distance from point F<sub>1</sub> to the line BF<sub>2</sub> is $b$.
(1) Find the equation of ellipse C;
(2) Let A<sub>1</sub> and A<sub>2</sub> be the two endpoints of the major axis of ellipse C, and point P is any point on ellipse C different from A<sub>1</sub> and A<sub>2</sub>. The line A<sub>1</sub>P intersects the line $x=m$ at point M. If the circle with MP as its diameter passes through point A<sub>2</sub>, find the value of the real number $m$.

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