
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 \( a \geqslant b \geqslant c \geqslant d \geqslant 0 \),
$$
\frac{a^{2}+b^{2}+c^{2}+d^{2}}{(a+b+c+d)^{2}}=\frac{3}{8}
$$
Find the maximum value of \( \frac{a+c}{b+d} \).

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