
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 \( a \geq b \geq c \geq d > 0 \) and \( a^{2} + b^{2} + c^{2} + d^{2} = \frac{(a + b + c + d)^{2}}{3} \), find the maximum value of \(\frac{a + c}{b + d}\).

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