
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 that positive integers \( a, b, c \) (where \( a \leq b \leq c \)) and real numbers \( x, y, z, w \) satisfy \( a^x = b^y = c^z = 70^w \) and \( \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{1}{w} \), find the value of \( c \).

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