
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
Let F($$\frac{1}{2}$$, 0), point A be on the x-axis, and point B be on the y-axis, with $$\overrightarrow{AM} = 2\overrightarrow{AB}$$ and $$\overrightarrow{BA} \cdot \overrightarrow{BF} = 0$$.  
(1) When point B moves on the y-axis, find the equation of the trajectory E of point M;  
(2) Let point P be a moving point on trajectory E, and points R, N be on the y-axis, with a circle $(x-1)^2 + y^2 = 1$ internally tangent to $\triangle PRN$. Find the minimum value of the area of $\triangle PRN$.

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