
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 real numbers \( a \), \( b \), \( c \), and \( d \) satisfying \( ad + bc = 1 \), determine the minimum value of 
\[ 
u = a^2 + b^2 + c^2 + d^2 + (a+c)^2 + (b-d)^2.
\]

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