
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
The side lengths of squares \( A, B, C, \) and \( D \) are \( 15, b, 10, d \) respectively (\( b \) and \( d \) are natural numbers). If their areas satisfy \( S_A = S_B + S_C + S_D \), then \( b + d = \) ______.

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