
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
Positive integers  $a$ ,  $b$ , and  $c$  are all powers of  $k$  for some positive integer  $k$ . It is known that the equation  $ax^2-bx+c=0$  has exactly one real solution  $r$ , and this value  $r$  is less than  $100$ . Compute the maximum possible value of  $r$ .

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