
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 $f(x)=x^{2}-a\ln x$.
1. If $f(x)$ is a monotonically decreasing function on the interval $[3,5]$, find the range of the real number $a$.
2. Let $g(x)=f(x)+(2+a)\ln x-2(b-1)x$, and suppose $x_{1}$ and $x_{2}$ $(x_{1} < x_{2})$ are two extremal points of the function $g(x)$. If $b\geqslant \frac {7}{2}$, find the minimum value of $g(x_{1})-g(x_{2})$.

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