
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 a moving point P and the two foci F<sub>1</sub>, F<sub>2</sub> of the hyperbola $$\frac {y^{2}}{9} - \frac {x^{2}}{16} = 1$$, the sum of the distances from P to F<sub>1</sub> and F<sub>2</sub> is 6$$\sqrt {5}$$,  
(1) Find the equation of the trajectory of point P;  
(2) If $$\overrightarrow {PF_{1}} \cdot \overrightarrow {PF_{2}} = 0$$, find the coordinates of point P;  
(3) Find the minimum value of the cosine of the angle ∠F<sub>1</sub>PF<sub>2</sub>.

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