
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
If the random variable $\xi$ follows a normal distribution $N(\mu,\sigma^{2})$, and $P(\mu-\sigma < \xi < \mu+\sigma)=0.6826$, $P(\mu-2\sigma < \xi < \mu+2\sigma)=0.9544$, suppose $\xi \sim N(1,\sigma^{2})$, and $P(\xi \geqslant 3)=0.1587$, in the Cartesian coordinate system $xOy$, if there are four points on the circle $x^{2}+y^{2}=\sigma^{2}$ whose distances to the line $12x-5y+c=0$ are $1$, then the range of the real number $c$ is __________.

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