
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
Say that a rational number is *special* if its decimal expansion is of the form  $0.\overline{abcdef}$ , where  $a$ ,  $b$ ,  $c$ ,  $d$ ,  $e$ , and  $f$  are digits (possibly equal) that include each of the digits  $2$ ,  $0$ ,  $1$ , and  $5$  at least once (in some order).  How many special rational numbers are there?


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