
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
Proof that there exist constant  $\lambda$ , so that for any positive integer  $m(\ge 2)$ , and any lattice triangle  $T$  in the Cartesian coordinate plane, if  $T$  contains exactly one  $m$ -lattice point in its interior(not containing boundary), then  $T$  has area  $\le \lambda m^3$ .
PS. lattice triangles are triangles whose vertex are lattice points;  $m$ -lattice points are lattice points whose both coordinates are divisible by  $m$ .

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