
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
The parabola  $\mathcal P$  given by equation  $y=x^2$  is rotated some acute angle  $\theta$  clockwise about the origin such that it hits both the  $x$  and  $y$  axes at two distinct points.  Suppose the length of the segment  $\mathcal P$  cuts the  $x$ -axis is  $1$ .  What is the length of the segment  $\mathcal P$  cuts the  $y$ -axis?

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