
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 five-digit number is called a "hill" if its first three digits are in ascending order and its last three digits are in descending order. For example, 13760 and 28932 are hills, whereas 78821 and 86521 are not hills. How many hills exist that are greater than the number 77777?

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