
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 a free sound field (open space) condition, the sound waves from a point sound source follow the spherical divergence law. At a distance of $r$ (unit: $m$) from the sound source, the amount of sound intensity attenuation is $\Delta L = 10\log(\frac{1}{4}\pi{r}^{2})$ (unit: $dB$).  
$(1)$ There are two sound detectors $A$ and $B$ located at distances of $20m$ and $50m$ from a certain sound source. How many decibels apart are their readings? (Round the result to $1dB$).  
$(2)$ Given a single sound source $O$, and two sound detectors $C$ and $D$ located on the same straight line, with a distance of $400m$ between $C$ and $D$. Assuming the readings of the two detectors are $61.05dB$ and $47.07dB$ respectively, find the distance between the source and detector $C$ (round to $1m$) and the sound intensity at the source (round to $1dB$).

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