
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
1. An arithmetic sequence is a sequence in which each term after the first is obtained from the previous term by adding a constant. For example, 3, 5, 7, 9, 11 is an arithmetic sequence with five terms.
(a) The first four terms of an arithmetic sequence are $20,13,6,-1$. What are the next two terms in the sequence?
(b) The numbers $2, a, b, c, 14$ in that order form an arithmetic sequence with five terms. What are the values of $a, b$, and $c$?
(c) The numbers 7, 15 and $t$, arranged in some unknown order, form an arithmetic sequence with three terms. Determine all possible values of $t$.
(d) The numbers $r, s, w, x, y, z$ in that order form an arithmetic sequence with six terms. The sequence includes the numbers 4 and 20, with the number 4 appearing before the number 20 in the sequence. Determine the largest possible value of $z-r$ and the smallest possible value of $z-r$.

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