
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 $f(x)=2\ln x-ax^{2}+1$,
(1) Find the range of values for $a$ if $f(x)$ has two zeros;
(2) There exists a real number $m$ such that the two zeros $\alpha$, $\beta$ of $f(x)=m$ both belong to the interval $[1,4]$, and $\beta-\alpha=1$, find the range of values for $a$.

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