
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
Let $a,$ $b,$ $c,$ $d$ be distinct real numbers such that the roots of $x^2 - 12ax - 13b = 0$ are $c$ and $d,$ and the roots of $x^2 - 12cx - 13d = 0$ are $a$ and $b.$ Find the value of $a + b + c + d.$

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