
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
On the board, the natural numbers \(a, b, c, d\) are written. It is known that among the six sums

\[ 
a+b, \quad b+c, \quad c+d, \quad d+a, \quad a+c, \quad b+d 
\]

three are equal to 23, and the other three are equal to 34.

(a) (1 point) What is the value of \(a+b+c+d\)?

(b) (3 points) What is the smallest of the numbers \(a, b, c, d\)?

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