
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
Let  $ \mathcal P$  be a parabola, and let  $ V_1$  and  $ F_1$  be its vertex and focus, respectively. Let  $ A$  and  $ B$  be points on  $ \mathcal P$  so that  $ \angle AV_1 B \equal{} 90^\circ$ . Let  $ \mathcal Q$  be the locus of the midpoint of  $ AB$ . It turns out that  $ \mathcal Q$  is also a parabola, and let  $ V_2$  and  $ F_2$  denote its vertex and focus, respectively. Determine the ratio  $ F_1F_2/V_1V_2$ .

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