
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 the function $f(x)=|x-1|$, the solution set of the inequality $f(x+5) \leqslant 3m (m > 0)$ is $[-7,-1]$  
$(1)$ Find the value of $m$;  
$(2)$ Given $a > 0$, $b > 0$, and $2a^{2}+b^{2}=3m$, find the maximum value of $2a \sqrt {1+b^{2}}$.

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