
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 $f(x)= \frac {a}{a^{2}-1}(a^{x}-a^{-x})$ $(a > 0$ and $a\neq 1)$,
(1) Determine the monotonicity of $f(x)$;
(2) Given that proposition $p$: the inequality $f(x)\leqslant 2b$ holds for any $x\in[-1,1]$, and proposition $q$: the two roots of the function $g(x)=x^{2}+(2b+1)x-b-1$ are respectively in the intervals $(-3,-2)$ and $(0,1)$, if $p\vee q$ is true and $p\wedge q$ is false, find the range of values for the real number $b$.

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