
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 $\overrightarrow{m}$ and $\overrightarrow{n}$ are unit vectors with an angle of $120^{\circ}$ between them, and the vector $\overrightarrow{a} = t\overrightarrow{m} + (1 - t)\overrightarrow{n}$, find the value of the real number $t$ such that $\overrightarrow{n} \perp \overrightarrow{a}$.

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