
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
3 points  $ O(0,\ 0),\ P(a,\ a^2), Q( \minus{} b,\ b^2)\ (a > 0,\ b > 0)$  are on the parabpla  $ y \equal{} x^2$ .
Let  $ S_1$  be the area bounded by the line  $ PQ$  and the parabola and let  $ S_2$  be the area of the triangle  $ OPQ$ .

Find the minimum value of  $ \frac {S_1}{S_2}$ .

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