
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 complex conjugate of a complex number $z$ is $\bar{z}$, if complex number $z_1=3+4i$, $z_2=t+i$, and ($z_1 \cdot \bar{z_2}$) is a real number, then the real number $t$ equals to ___.

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