
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
Transform the expression \(\left|\frac{x^{2}-6 x+9}{3-x}+\frac{4 x^{2}-5 x}{x}\right|=\left|\frac{(3-x)^{2}}{3-x}+\frac{x(4 x-5)}{x}\right|=|3 x-2|\), yielding \(f(x)=|3 x-2|\), \(D(f): x \neq 3, x \neq 0\).

Solve the equation \(|3 x-2|=|x+a|\) graphically in the system \(x O a\). \((3 x-2)^{2}=(x+a)^{2}\)

\[
\begin{gathered}
(3 x-2+x+a)(3 x-2-x-a)=0 \\
{\left[\begin{array}{l}
4 x-2+a=0 \\
2 x-2-a=0
\end{array}\right.} \\
{\left[\begin{array}{c}
a=-4 x+2 \\
a=2 x-2
\end{array}\right.}
\end{gathered}
\]

The equation \(f(x)=p(x)\) has exactly one solution when \(a=-10\);

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