
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 $\overrightarrow{a_{1}}=2 \overrightarrow{m}- \overrightarrow{j}+ \overrightarrow{k}$, $\overrightarrow{a_{2}}= \overrightarrow{m}+3 \overrightarrow{j}-2 \overrightarrow{k}$, $\overrightarrow{a_{3}}=-2 \overrightarrow{m}+ \overrightarrow{j}-3 \overrightarrow{k}$, $\overrightarrow{a_{4}}=3 \overrightarrow{m}+2 \overrightarrow{j}+5 \overrightarrow{k}$, where $\overrightarrow{m}, \overrightarrow{j}, \overrightarrow{k}$ are pairwise orthogonal unit vectors, determine the values of the real numbers $λ$, $μ$, $ν$ such that $\overrightarrow{a_{4}}=λ \overrightarrow{a_{1}}+μ \overrightarrow{a_{2}}+ν \overrightarrow{a_{3}}$.

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