
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 $f(x)=(x+1)\ln x$.  
$(1)$ Find the equation of the tangent line to $f(x)$ at $x=1$;  
$(2)$ Let $g(x)= \frac {1}{a(1-x)}f(x)$, for any $x\in(0,1)$, $g(x) < -2$, find the range of the real number $a$.

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