
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 sets $A=\{a^{2}, a+1, -3\}$ and $B=\{a-3, 2a-1, a^{2}+1\}$, if $A\cap B=\{-3\}$.<br/>$(Ⅰ)$ Find the value of the real number $a$;<br/>$(Ⅱ)$ Let the value of the quadratic function $y=x^{2}-4x+6$ at $x=-a$ be $m$, solve the inequality $x^{2}-4x+6 \gt m$.

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