
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 $\overrightarrow{i}, \overrightarrow{j}$ are orthogonal unit vectors, and vectors $\overrightarrow{a} = (m+1)\overrightarrow{i} - 3\overrightarrow{j}, \overrightarrow{b} = \overrightarrow{i} + (m-1)\overrightarrow{j}$, if $(\overrightarrow{a} + \overrightarrow{b}) \perp (\overrightarrow{a} - \overrightarrow{b})$, determine the value of the real number $m$.

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