
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
Let proposition $p$: The inequality $|x-1|+|x-3| > a$ holds for all real numbers $x$; proposition $q$: Given the function $f(x)=mx^{3} +nx^{2}$, the tangent line at the point $(-1,2)$ is exactly parallel to the line $2x+y=1$, and $f(x)$ is monotonically decreasing on the interval $[a,a+1]$. If proposition $p$ or $q$ is true, find the range of the real number $a$.

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