
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 $f(x)=e^{x}(ax^{2}+x+1)$, the tangent line of the curve $y=f(x)$ at $x=1$ is parallel to the $x$-axis, and $|f(\cos θ)-f(\sin θ)| \leqslant b$ always holds for all $θ∈[0, \frac{π}{2}]$. Find the minimum value of $b$.

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