
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 propositions $p$: $x\_1$, $x\_2$ are the two real roots of the equation $x^{2}-mx-1=0$, and the inequality $a^{2}+4a-3\leqslant |x\_{1}-x\_{2}|$ holds for any $m\in R$; and proposition $q$: the inequality $x^{2}+2x+a < 0$ has a solution. If proposition $p\vee q$ is true and proposition $p\wedge q$ is false, find the range of values for $a$.

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