
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
Given that the square root of $a$ is $\pm 3$, the cube root of $2b+4$ is $2$, and $\sqrt[3]{c}=\sqrt{-c}$. Find:<br/>
$(1)$ The value of $a+b$;<br/>
$(2)$ The square root of $a+2b+c$.

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