
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
A line segment AB of fixed length 3 has its endpoints A and B sliding on the x-axis and y-axis, respectively. A moving point P satisfies $\overrightarrow{BP} = 2\overrightarrow{PA}$.  
(Ⅰ) Find the equation of the trajectory curve C of point P;  
(Ⅱ) If a line passing through the point (1, 0) intersects curve C at points M and N, find the maximum value of $\overrightarrow{OM} \cdot \overrightarrow{ON}$.

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