
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
If \( a, b, c, x, y, \) and \( z \) are positive numbers such that \( a^2 + b^2 + c^2 = 49, \) \( x^2 + y^2 + z^2 = 64, \) and \( ax + by + cz = 56, \) find the value of \( k \) where \( a = kx, b = ky, c = kz. \)

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