
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
Define a 4-digit number as a "double peak mountain number" if its middle two digits are equal and both are greater than the digits on either side. For example, 37273 is a double peak mountain number. How many 4-digit double peak mountain numbers are there?

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