
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 \( +1+3+9+27+81+243+729 \), you may cross out any terms and change the signs of some of the remaining numbers from "+" to "-". Masha wants to first obtain an expression equal to 1, then start over and obtain an expression equal to 2, then again start over and obtain an expression equal to 3, and so on. Up to what highest integer can she achieve this consecutively without skipping any values?

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