
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 two lines $l_1: x+3y-3m^2=0$ and $l_2: 2x+y-m^2-5m=0$ intersect at point $P$ ($m \in \mathbb{R}$).  
(1) Express the coordinates of the intersection point $P$ of lines $l_1$ and $l_2$ in terms of $m$.  
(2) For what value of $m$ is the distance from point $P$ to the line $x+y+3=0$ the shortest? And what is the shortest distance?

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