
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
A positive integer hides another number when, by deleting some of its digits, the other number appears. For example, the number 123 hides the numbers 1, 2, 3, 12, 13, and 23, but does not hide 32, 123, and 213.

a) What is the largest three-digit number hidden by 47239?
b) What is the smallest number that simultaneously hides 2009 and 9002?
c) Find a multiple of 2009 that hides 2009 and whose units digit is 3.

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