
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 $$A\left( \frac {1}{4}, 0\right)$$, a moving point P is 1 unit closer to point A than to the line $$x = -\frac {5}{4}$$.  
(1) Find the equation of the trajectory of point P;  
(2) Given M(4, 0), is there a fixed line $$x = a$$ such that the circle with diameter PM intersects the line $$x = a$$ at a chord of fixed length? If so, find the equation of the fixed line; if not, explain why.

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