
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
A line $l$ passes through the left focus $F$ of the hyperbola $C$: $$\frac {x^{2}}{a^{2}} - \frac {y^{2}}{b^{2}} = 1$$ ($a > 0$, $b > 0$) and intersects the right branch of the hyperbola $C$ at point $P$. If $l$ is tangent to the circle $x^{2} + y^{2} = a^{2}$ exactly at the midpoint of segment $FP$, then the slope of line $l$ is \_\_\_\_\_\_.

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