
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
The length of a railway line is $77.7 \mathrm{~km}$. Along the track, at every entire hectometer, there is a stone that marks the distance from both endpoints in kilometers, for example: $0.0 \star 77.7$, or $1.2 \star 76.5$.

a) How many stones have markings where only two different digits appear?

b) How many stones have markings where no digit appears more than once?

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