
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 $f(x) = a^x + b^x - c^x$, where $c > a > 0$, $c > b > 0$.

(1) Define the set $M = \{(a, b, c) | a, b, c$ cannot form the sides of a triangle, and $a = b\}$. The set of values for the roots of $f(x)$ corresponding to the elements $(a, b, c) \in M$ is _______________.

(2) Suppose $a, b,$ and $c$ are the lengths of the sides of triangle $\triangle ABC$, then the correct conclusion(s) from the following are _______________. (Fill in the number(s))
  ① For any $x \in (-\infty, 1), f(x) > 0$
  ② There exists $x \in \mathbb{R}$ such that $a^x, b^x, c^x$ cannot form the sides of a triangle
  ③ If $\triangle ABC$ is an obtuse triangle, then there exists $x \in (1, 2)$ such that $f(x) = 0$

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