
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
If a person lives on the even-numbered side of the street and the sum of all house numbers on one side of their house equals the sum of the house numbers on the other side, how many houses are on this side of the street and what is their house number?

We assume that there are more than 50 and fewer than 500 houses on each side of the street.

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