
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  $f$ , defined on the set of ordered pairs of positive integers, satisfies the following properties:
\begin{eqnarray*} f(x,x) &=& x,  f(x,y) &=& f(y,x), \quad \text{and}  (x + y) f(x,y) &=& yf(x,x + y). \end{eqnarray*}
Calculate  $f(14,52)$ .

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