
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 two unit vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ with an angle of 60° between them, the vector $\overrightarrow{c} = (1-t)\overrightarrow{a} + t\overrightarrow{b}$. Find the value of $t$ given that $\overrightarrow{b} \cdot \overrightarrow{c} = -\frac{1}{2}$.

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