
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 vectors $\overrightarrow{a} = m\overrightarrow{i} + 5\overrightarrow{j} - \overrightarrow{k}$ and $\overrightarrow{b} = 3\overrightarrow{i} + \overrightarrow{j} + r\overrightarrow{k}$, if $\overrightarrow{a} \parallel \overrightarrow{b}$, then the product of the real numbers $m \cdot r =$ ______.

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