
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 real numbers \( x \) and \( y \) satisfying \( 3x^2 + 4y^2 = 1 \). If the value of \( |3x + 4y - \lambda| + |\lambda + 7 - 3x - 4y| \) is independent of \( x \) and \( y \), what is the range of \(\lambda\)?

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