
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 tangent line to the circle $x^{2}+y^{2}=1$ intersects the ellipse $\frac{x^{2}}{4}+\frac{y^{2}}{3}=1$ at two points A and B. The tangent lines to the ellipse at points A and B intersect at point P. Find the equation of the locus of point P.

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