
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 sets A, B, and C defined as follows:
- $A=\{x \in \mathbb{Z} \mid \left| x \right| \leq 4\}$,
- $B=\{x \mid (x-1)(x^2-5x+6)=0\}$,
- $C=\{a \mid y= (a^2-7a+13)x^a \text{ is a power function}\}$,

Calculate:
(1) Sets A, B, and C;
(2) $C_A \backslash [C_A(B) \cup C_A(C)]$.

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