
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 tram ticket is called "lucky in Leningrad style" if the sum of its first three digits is equal to the sum of its last three digits. A tram ticket is called "lucky in Moscow style" if the sum of its digits in even positions is equal to the sum of its digits in odd positions. How many tickets are there that are both lucky in Leningrad style and lucky in Moscow style, including the ticket 000000?

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