
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 $f(x) = \frac{2tx^2 + \sqrt{2}t\sin\left(x + \frac{\pi}{4}\right) + x}{2x^2 + \cos x}$ with respect to $x$, its maximum value is $a$ and its minimum value is $b$. If $a+b=2$, then the value of the real number $t$ is \_\_\_\_\_\_.

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