
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
Let the function $f(x) = ax + bx - cx$, where $c > a > 0$, $c > b > 0$. If $a$, $b$, $c$ are the lengths of the sides of $\triangle ABC$, then the correct conclusion(s) is/are __________.  
① For any $x \in (-\infty, 1)$, $f(x) < 0$;  
② There exists $x \in \mathbb{R}$, such that $ax$, $bx$, $cx$ cannot form the lengths of the sides of a triangle;  
③ If $\triangle ABC$ is an obtuse triangle, there exists $x \in (1, 2)$ such that $f(x) = 0$.

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