
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 a sequence {a_n} where the sum of its first n terms is S_n, and it satisfies the equation S_n = a_n^2 + bn (a and b are constants), with a_9 = π/2. Let the function f(x) = 2 + sin(2x) - 2sin^2(x/2), and denote y_n = f(a_n). Calculate the sum of the first 17 terms of the sequence {y_n}.

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