
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
In the $xOy$ coordinate plane, the curve
$$
y=(3 x-1)\left(\sqrt{9 x^{2}-6 x+5}+1\right)+(2 x-3)\left(\sqrt{4 x^{2}-12 x+13}+1\right)
$$

intersects the $x$-axis at the point $\qquad$ .

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