
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
The function $f$ is defined for all ordered pairs of positive integers with the following properties:
\begin{align*}
f(x, x) &= x, \\
f(x, y) &= f(y, x), \\
(x + y) f(x, y) &= y f(x, x + y).
\end{align*}
Calculate $f(17, 69)$.

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