
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 that the arithmetic sequence {a<sub>n</sub>} has a common difference of d, and the sum of its first n terms is S<sub>n</sub>. If a<sub>4</sub> + a<sub>10</sub> = 0 and 2S<sub>12</sub> = S<sub>2</sub> + 10, find the value of d.

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