
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 $f(x)=\sqrt{x^2+2x+1}-|x-m|$ has a maximum value of 4 (where $m>0$).  
(1) Find the value of $m$;  
(2) If $a^2+b^2+c^2=m$, find the minimum value of $\frac{1}{a^2}+\frac{1}{b^2}+\frac{4}{c^2}$.

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