
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
A triangle has sides of length  $48$ ,  $55$ , and  $73$ .  A square is inscribed in the triangle such that one side of the square lies on the longest side of the triangle, and the two vertices not on that side of the square touch the other two sides of the triangle.  If  $c$  and  $d$  are relatively prime positive integers such that  $c/d$  is the length of a side of the square, find the value of  $c+d$ .

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