
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
How many numbers between 100 and 999 (inclusive) have digits that form an arithmetic progression when read from left to right?

A sequence of three numbers \( a, b, c \) is said to form an arithmetic progression if \( a + c = 2b \). 

A correct numerical answer without justification will earn 4 points. For full points, a detailed reasoning is expected.

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