
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
Read the following material and answer the question:  
$(2x-5)^{2}+\left(3x+7\right)^{2}=\left(5x+2\right)^{2}$  
Let $m=2x-5$, $n=3x+7$, then $m+n=5x+2$  
The original equation can be transformed into $m^{2}+n^{2}=\left(m+n\right)^{2$  
Therefore, $mn=0$, i.e. $\left(2x-5\right)\left(3x+7\right)=0$  
Solving it, we get $x_{1}=\frac{5}{2},x_{2}=-\frac{7}{3}$.  
Therefore, the solution set of the inequality $\left(2x-5\right)^{2}+\left(3x+7\right)^{2} \gt \left(5x+2\right)^{2}$ is $\{x|-\frac{7}{3}＜x＜\frac{5}{2}\}$.  
Please use the above method to solve the inequality $\left(4x-5\right)^{2}+\left(3x-2\right)^{2} \lt \left(x-3\right)^{2}$.

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