
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 the magnitude of vector $\overrightarrow{p}$ is $\sqrt{2}$, the magnitude of vector $\overrightarrow{q}$ is 1, and the angle between $\overrightarrow{p}$ and $\overrightarrow{q}$ is $\frac{\pi}{4}$, $\overrightarrow{a} = 3\overrightarrow{p} + 2\overrightarrow{q}$, $\overrightarrow{b} = \overrightarrow{p} - \overrightarrow{q}$. Find the length of the shorter diagonal of the parallelogram formed by $\overrightarrow{a}$ and $\overrightarrow{b}$ as adjacent sides.

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