
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
In the Cartesian coordinate system xOy, point P (x, y) satisfies the condition $\overrightarrow{a} \cdot \overrightarrow{b} = 3$, where $\overrightarrow{a} = (2x+3, y)$ and $\overrightarrow{b} = (2x-3, 3y)$.
(1) Find the equation of the trajectory of point P.
(2) A line l passes through point F (0, 1) and intersects the trajectory of point P at two points A and B. If $|AB| = \frac{16}{5}$, find the equation of line l.

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