
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
(The full score of this question is 14 points) It is known that A and B are two fixed points on a plane, and the moving point P satisfies $|PA| + |PB| = 2$.
(1) Find the equation of the trajectory of point P;
(2) Suppose the line $l: y = k (k > 0)$ intersects the trajectory of point P from (1) at points M and N, find the maximum area of $\triangle BMN$ and the equation of line $l$ at this time.

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