
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
Three non-collinear lattice points  $A,B,C$  lie on the plane  $1+3x+5y+7z=0$ . The minimal possible area of triangle  $ABC$  can be expressed as  $\frac{\sqrt{m}}{n}$  where  $m,n$  are positive integers such that there does not exists a prime  $p$  dividing  $n$  with  $p^2$  dividing  $m$ . Compute  $100m+n$ .

*Proposed by Yannick Yao*

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