
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
Let  $ABC$  be a triangle in the coordinate plane with vertices on lattice points and with  $AB = 1$ .  Suppose the perimeter of  $ABC$  is less than  $17$ .  Find the largest possible value of  $1/r$ , where  $r$  is the inradius of  $ABC$ .

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