
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 $f(x)=e^{x}-e^{-x}+x^{3}+3x$, if $f(2a-1)+f(b-1)=0$ $(a > 0,b > 0)$, then the minimum value of $\dfrac {2a^{2}}{a+1}+ \dfrac {b^{2}+1}{b}$ is \_\_\_\_\_\_.

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