
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 $f(x)=|x+1|-|x|$, let its maximum value be $m$.
(1) Find the value of $m$;
(2) If $a$ and $b$ are positive real numbers such that $a+b=m$, find the minimum value of $\dfrac {a^{2}}{b+1}+ \dfrac {b^{2}}{a+1}$.

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