
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 non-zero vectors $a$ and $b$ that are not collinear, let $\overrightarrow{OA} = a$, $\overrightarrow{OB} = tb$ ($t \in \mathbb{R}$), and $\overrightarrow{OC} = \frac{1}{3}(a + b)$. Determine the value of the real number $t$ when points $A$, $B$, and $C$ are collinear.

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