
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 the sequence $\{a_n\}$ satisfies: $a_1=1, a_2=2, a_{n+2}=a_{n+1}-a_{n} (n\in\mathbb{N}^*)$, and the function $f(x)=ax^3+b\tan x$, if $f(a_4)=9$, then the value of $f(a_1)+f(a_{2017})$ is ______.

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