
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 the real numbers \( a \geq b \geq c \geq d \) with \( a + b + c + d = 9 \) and \( a^2 + b^2 + c^2 + d^2 = 21 \), find the minimum possible value of \( \text{ab} - \text{cd} \).

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