
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
Let \( c^2 = \frac{25}{81} \) and \( d^2 = \frac{(\sqrt{3} - 1)^2}{9} \), where \( c \) is a negative real number and \( d \) is a positive real number. If \( (c-d)^2 \) can be expressed in the simplified form \( \frac{x\sqrt{y}}{z} \) where \( x, y, \) and \( z \) are positive integers, what is the value of the sum \( x+y+z \)?

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