
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
 We say that a polygon  $P$  is inscribed in another polygon  $Q$  when all the vertices of  $P$  belong to the perimeter of  $Q$ . We also say in this case that  $Q$  is circumscribed to  $P$ . Given a triangle  $T$ , let  $\ell$  be the largest side of a square inscribed in  $T$   and  $L$  is the shortest side of a square circumscribed to  $T$  . Find the smallest possible value of the ratio  $L/\ell$  .

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