
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 parametric equation of line l₁ as $$\begin{cases} \overset{x=t+a}{y=t-3}\end{cases}$$ (where t is a parameter and a < 0), a polar coordinate system is established with the origin of the rectangular coordinate system as the pole and the positive semi-axis of the x-axis as the polar axis. The polar equation of circle C is ρ = 4cosθ.

1. If the length of the chord intercepted by line l₁ on circle C is 2$$\sqrt {2}$$, find the value of a.
2. The parametric equation of line l₂ is $$\begin{cases} \overset{x=2+tcos\theta }{y=tsin\theta }\end{cases}$$ (where t is a parameter). If l₁ is perpendicular to l₂ and P is the foot of the perpendicular, find the polar coordinates of P.

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