
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
Q. A light source at the point  $(0, 16)$  in the co-ordinate plane casts light in all directions. A disc(circle along ith it's interior) of radius  $2$  with center at  $(6, 10)$  casts a shadow on the X-axis. The length of the shadow can be written in the form  $m\sqrt{n}$  where  $m, n$  are positive integers and  $n$  is squarefree. Find  $m + n$ .

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