
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
Determine the largest and smallest fractions  $F = \frac{y-x}{x+4y}$  
if the real numbers  $x$  and  $y$  satisfy the equation  $x^2y^2 + xy + 1 = 3y^2$ .

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