
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
144. Find the triangle with the smallest possible perimeter, given the following information:

a) Two vertices $A$ and $B$ of the triangle and a line $l$ on which the third vertex lies;
b) A vertex $A$ and two lines $l$ and $m$ on which the vertices $B$ and $C$ lie;
c) Three lines $l$, $m$, $n$ on which the vertices $A$, $B$, and $C$ lie.

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