
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 function $f(x) = \frac{x^{3}+tx^{2}+\sqrt{2}t\sin(x+\frac{\pi}{4})+2t}{x^{2}+2+\cos x}\ (t \neq 0)$, where $m$ is the maximum value and $n$ is the minimum value, and $m + n = 2017$, find the value of the real number $t$.

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