
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 $f(x)=x-1-a\ln x$.
- $(1)$ If $f(x) \geqslant 0$, find the value of $a$;
- $(2)$ Let $m$ be an integer, and for any positive integer $n$, $(1+ \frac {1}{2})(1+ \frac {1}{2^{2}})\ldots(1+ \frac {1}{2^{n}}) < m$, find the minimum value of $m$.

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