
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 that vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are orthogonal (perpendicular) with $|\overrightarrow{a}|=2$ and $|\overrightarrow{b}|=3$, and the vector $3\overrightarrow{a}+2\overrightarrow{b}$ is orthogonal to $\lambda\overrightarrow{a}-\overrightarrow{b}$, find the value of the real number $\lambda$. The options are:
A) ${±}\dfrac{3}{2}$
B) ${-}\dfrac{3}{2}$
C) $\dfrac{3}{2}$
D) $1$

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