
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
Let the function $f(x)=\begin{cases} & (x+a)\ln x, & x > 0 \\ & 2ax+2+a, & x\leqslant 0 \end{cases}$, and $f'(-1)=f'(1)$, then when $x > 0$, the minimum value of the derivative of $f(x)$, $f'(x)$, is ______.

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