
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 that the left and right foci of the ellipse $\frac{x^2}{a^2}+ \frac{y^2}{b^2}=1$ are $F_1$ and $F_2$ respectively, determine the value of the product $d_1 \cdot d_2$ where $d_1$ and $d_2$ denote the distances from $F_1$ and $F_2$ to a tangent line $l$ drawn at any point $P$ on the ellipse.

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