
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 $f(x)=a\sin x - b\cos x$ where $a$ and $b$ are constants, and $a \neq 0$, for $x \in \mathbb{R}$, reaches its minimum value at $x= \frac{\pi}{4}$, determine the symmetry of the function $y=f\left(\frac{3\pi}{4}-x\right)$.

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