
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 points A (-1, 0), B (1, 0), and line AM intersects line BM at point M. The slopes of line AM and line BM are denoted as $k_{AM}$ and $k_{BM}$, respectively, and $k_{AM} \cdot k_{BM} = -2$  
(Ⅰ) Find the equation of the trajectory C of point M;  
(Ⅱ) A line PQ passes through a fixed point F (0, 1) and intersects curve C at points P and Q. Does the area of $\triangle OPQ$ have a maximum value? If it exists, find the maximum area of $\triangle OPQ$; if not, explain why.

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