
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
In the rectangular coordinate system $xOy$, if the distance from the focus of the hyperbola $x^{2}- \frac{y^{2}}{b^{2}}=1(b > 0)$ to its asymptote is equal to the distance from the point $M(1,2)$ on the parabola $y^{2}=2px$ to its focus, then the real number $b=$ _____ .

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