
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 $$C: \frac {x^{2}}{25}+ \frac {y^{2}}{9}=1$$, the line $l$ intersects the ellipse $C$ at two distinct points $A$ and $B$. $P$ is the midpoint of chord $AB$.  
(1) If the slope of line $l$ is $$\frac {4}{5}$$, find the equation of the trajectory of point $P$.  
(2) Does there exist a line $l$ such that the chord $AB$ is exactly bisected by the point $$( \frac {4}{3},- \frac {3}{5})$$? If it exists, find the equation of line $l$; if not, explain why.

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