
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
If the domain of $f(x) = \lg (x^2 - ax + b)$ is $M = \{x \mid x < 1 \text{ or } x > 3\}$, and the domain of $\varphi(x) = \sqrt{(a - x)(x - b)}$ is $P$, then $M \cap P = \quad$.

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