
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 $A(-1,0)$ and $B(1,0)$, lines $AM$ and $BM$ intersect at point $M$, and $k_{MA} \times k_{MB} = -2$.
(1) Find the equation of the trajectory $C$ of point $M$;
(2) A line $PQ$ passing through the fixed point $F(0,1)$ intersects the curve $C$ at points $P$ and $Q$. Does the area of $\triangle OPQ$ have a maximum value? If so, find the maximum area of $\triangle OPQ$. If not, explain the reason.

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