
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  $T$  be a triangle with side lengths  $26$ ,  $51$ , and  $73$ . Let  $S$  be the set of points inside  $T$  which do not lie within a distance of  $5$  of any side of  $T$ . Find the area of  $S$ .

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