
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 $p$ and $q$: Proposition $p$ states that the inequality $x^{2}+ax-2 > 0$ holds true for $x \in [1,2]$; Proposition $q$ states that the function $f(x)=\log_{\frac{1}{3}}(x^{2}-2ax+3a)$ is a decreasing function on the interval $[1, +\infty)$. If the proposition "$p \vee q$" is true, find the range of values for the real number $a$.

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