
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 positive real numbers \(a, b, c, d\) that satisfy the equalities

\[ a^{2} + d^{2} - a d = b^{2} + c^{2} + b c \quad \text{and} \quad a^{2} + b^{2} = c^{2} + d^{2} \]

find all possible values of the expression \(\frac{a b + c d}{a d + b c}\).

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