
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 $f(x) = x^2 + x\sin x + \cos x$.

(1) If the curve $y = f(x)$ is tangent to the line $y = b$ at the point $(a, f(a))$, find the values of $a$ and $b$;

(2) If the curve $y = f(x)$ intersects the line $y = b$ at two distinct points, find the range of values for $b$.

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