
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 the functions $f(x)$ and $g(x)$ satisfy $f(1) = 1$, $f'(1) = 1$, $g(1) = 2$, and $g'(1) = 1$, then the equation of the tangent line to the graph of the function $$F(x) = \frac{f(x) - 2}{g(x)}$$ at $x = 1$ is \_\_\_\_\_\_.

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