
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
(a) Three of the five numbers \(2,5,10,13,15\) can be chosen to form an arithmetic sequence with three terms. What are the three numbers?

(b) The numbers \(p, 7, q, 13\), in that order, form an arithmetic sequence with four terms. Determine the value of \(p\) and the value of \(q\).

(c) The numbers \(a, b, c, (a+21)\), in that order, form an arithmetic sequence with four terms. Determine the value of \(c-a\).

(d) The numbers \((y-6), (2y+3), \left(y^{2}+2\right)\), in that order, form an arithmetic sequence with three terms. Determine all possible values of \(y\).

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