
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 a real number $a$ satisfying $1 < a < 2$, let proposition $p$ be: the function $y=\log_{a}(2-ax)$ is decreasing on the interval $[0,1]$, and proposition $q$ be: "$|x| < 1$" is a sufficient but not necessary condition for "$x < a$". Then, the correct statement among the following is:

① Either $p$ or $q$ is true; ② Both $p$ and $q$ are false; ③ $p$ is false and $q$ is true; ④ Either $p$ is false or $q$ is false.

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