
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 straight line
$$
\begin{cases}
x = 1 - t \\
y = 2t
\end{cases}
\quad (t \in \mathbb{R} \text{ is the parameter})
$$
is tangent to the circle
$$
\begin{cases}
x = \cos \theta \\
y = \sin \theta + a
\end{cases}
\quad (0 \leq \theta < 2\pi, \theta \text{ is the parameter}, a \text{ is a constant and } a > 0)
$$
find the value of $a$.

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