
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
Suppose that \(a, b, c, d\) are real numbers satisfying \(a \geq b \geq c \geq d \geq 0\), \(a^2 + d^2 = 1\), \(b^2 + c^2 = 1\), and \(ac + bd = \frac{1}{3}\). Find the value of \(ab - cd\).

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