
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 \( n \) is called "flippant" if \( n \) does not end in \( 0 \) (when written in decimal notation) and, moreover, \( n \) and the number obtained by reversing the digits of \( n \) are both divisible by \( 7 \). How many flippant integers are there between \( 10 \) and \( 1000 \)?

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