
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
We randomly choose two points independently on the interval $(0,1)$ of the number line. (Choosing a point $P$ randomly in the interval $(a, b)$ means that for any subinterval $(c, d)$ of $(a, b)$, the probability that $P$ falls in $(c, d)$ is equal to $\frac{d-c}{b-a}$.)

We know that the probability that the distance between the two chosen points is less than $h$ falls between ${1/4}$ and $3/4$.

Within what boundaries does $h$ lie?

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