
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 $f(x)=(x-a)\ln{x}$, where $a \geq 0$,
(1) When $a=0$, if the line $y=2x+m$ is tangent to the graph of $y=f(x)$, find the value of $m$;
(2) If $f(x)$ is a monotonically decreasing function on the interval $[1,2]$, find the minimum value of $a$.

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