
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
In the Cartesian coordinate plane $(xOy)$, let points $A(1,0)$, $B(0,1)$, $C(a,b)$, and $D(c,d)$. If the inequality ${\overrightarrow{{CD}}}^{2}\geqslant (m-2)\overrightarrow{{OC}}\cdot\overrightarrow{{OD}}+m(\overrightarrow{{OC}}\cdot\overrightarrow{{OB}})\cdot(\overrightarrow{{OD}}\cdot\overrightarrow{{OA}})$ holds for any real numbers $a$, $b$, $c$, and $d$, then the maximum value of the real number $m$ is $\_\_\_\_\_.$

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