
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 points $A(2,3)$, $B(6,-3)$, and point $P$ on the line $3x-4y+3=0$, if there are two points $P$ that satisfy the equation $\overrightarrow{AP} \cdot \overrightarrow{BP}+2\lambda =0$, then the range of the real number $\lambda$ is \_\_\_\_\_\_\_\_.

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