
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: The curve $C$ has the polar coordinate equation: $ρ=a\cos θ (a>0)$, and the line $l$ has the parametric equations: $\begin{cases}x=1+\frac{\sqrt{2}}{2}t\\y=\frac{\sqrt{2}}{2}t\end{cases}$ ($t$ is the parameter)

1. Find the Cartesian equation of the curve $C$ and the line $l$;
2. If the line $l$ is tangent to the curve $C$, find the value of $a$.

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