
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) Find the value of $a$ such that $f(x) \geqslant 0$;
(2) Let $m$ be an integer, and for any positive integer $n$, $(1+\frac{1}{2})(1+\frac{1}{2^{2}})\dots(1+\frac{1}{2^{n}}) < m$, find the minimum value of $m$.

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