
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
If the line passing through points P(0, 2) and Q(1, 3) has the parametric equation $$\begin{cases} x=t+a, \\ y=\frac{b}{2}t+1 \end{cases}$$ (where $t$ is the parameter, and $a$, $b$ are constants), determine the values of $a$ and $b$.

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