
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 non-coplanar plane vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ with magnitudes $|\overrightarrow{a}|=3$ and $|\overrightarrow{b}|=2$, let vector $\overrightarrow{c} = λ\overrightarrow{a} + μ\overrightarrow{b}$ where $λ, μ ∈ ℝ$ and $λ + μ = 1$. If $\frac{\overrightarrow{c} \cdot \overrightarrow{b}}{|\overrightarrow{b}|} = \frac{\overrightarrow{c} \cdot \overrightarrow{a}}{|\overrightarrow{a}|}$, find the value of $λ$.

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