
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 non-zero vectors $\overrightarrow{m}$ and $\overrightarrow{n}$ satisfy $3|\overrightarrow{m}|=2|\overrightarrow{n}|$ and the angle between $\overrightarrow{m}$ and $\overrightarrow{n}$ is $60^{\circ}$. If $\overrightarrow{n} \perp (t\overrightarrow{m} + \overrightarrow{n})$, determine the value of the real number $t$.

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