
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
In the sum \(1+3+9+27+81+243+729 \), one can strike out any terms and change some signs in front of the remaining numbers from "+" to "-". Masha wants to get an expression equal to 1 in this way, then (starting from scratch) get an expression equal to 2, then (starting again from scratch) get 3, and so on. Up to what maximum integer will she be able to do this without skipping any numbers?

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