
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
Define the operation on R as: $|{\begin{array}{l}a&b\\ c&d\end{array}}|=ad-bc$. If the inequality $|{\begin{array}{l}{x-1}&{a-2}\\{a+1}&x\end{array}}|≥1$ holds for any real number x, determine the minimum value of the real number a.

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