
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
Given positive integers \(a, b,\) and \(c\) that satisfy \(2017 \geq 10a \geq 100b \geq 1000c\), determine how many such ordered triples \((a, b, c)\) exist.

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