
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
In the rectangular coordinate system, establish a polar coordinate system with the origin as the pole, the positive semi-axis of the x-axis as the polar axis, and the same unit length. Given that the polar coordinate equation of line $l$ is $\sqrt {2}ρ\cos(θ+ \frac {π}{4})=1$, and the polar coordinate equation of curve $C$ is $ρ=2a\cosθ$, where $a>0$:
(1) Let $t$ be a parameter. If $y= \frac { \sqrt {2}}{2}t-1$, find the parametric equation of line $l$;
(2) It is known that line $l$ intersects curve $C$ at points $P$ and $Q$. Let $M(0,−1)$, and $|PQ|^2=4|MP|⋅|MQ|$. Find the value of real number $a$.

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