
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 set $A=\{x \mid y=\lg(1-x)\}$ and set $B$ is the range of the function $f(x) = -x^2 + 2x + m$ where $m\in \mathbb{R}$.

(1) Represent sets $A$ and $B$ using intervals.
(2) Find the range of values for $m$ such that $A \cap B = A$.

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