
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
For a number $x$, we use $\left(x\right]$ to represent the largest integer less than $x$. For example, $\left(2.6\right]=2$, $\left(-3\right]=-4$, $\left(10\right]=9$; if $\left(a\right]$ and $\left(b\right]$ are additive inverses of each other, then the maximum value of the expression $a+b$ is ______.

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