
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 $f(x)=x^{2}-ax-\ln x$, where $a\in\mathbb{R}$.
(I) If the slope of the tangent line to the graph of the function $f(x)$ at $x=1$ is $1$, find the value of the real number $a$;
(II) When $a\geqslant -1$, let $H$ denote the minimum value of $f(x)$, find the maximum value of $H$.

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