
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
(10 points) Find the equation of the line that passes through the intersection point M of lines $L_1: 3x + 4y - 5 = 0$ and $L_2: 2x - 3y + 8 = 0$, and satisfies the following conditions: (1) It is parallel to the line $2x + y + 5 = 0$; (2) It is perpendicular to the line $2x + y + 5 = 0$.

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