
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
Source: 2017 Canadian Open Math Challenge, Problem B4
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Numbers  $a$ ,  $b$  and  $c$  form an arithmetic sequence if  $b - a = c - b$ . Let  $a$ ,  $b$ ,  $c$  be positive integers forming an arithmetic sequence with  $a < b < c$ . Let  $f(x) = ax2 + bx + c$ . Two distinct real numbers  $r$  and  $s$  satisfy  $f(r) = s$  and  $f(s) = r$ . If  $rs = 2017$ , determine the smallest possible value of  $a$ .

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