
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 the function $f(x)$, if there exists an interval $\left[m,n\right]$, satisfying the following conditions: ① $f(x)$ is monotonically increasing on $\left[m,n\right]$; ② when the domain of $f(x)$ is $\left[m,n\right]$, the range of $f(x)$ is $\left[2m,2n\right]$, then $\left[m,n\right]$ is called the "multiple interval" of the function. If the function $f(x)=\sqrt{x+1}+a$ has a "multiple interval", then the range of $a$ is ______.

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