
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
In the coordinate plane, point $D(0,p)$ lies on the $y$-axis between $P(0,15)$ and $O(0,0)$. There is a point $E(15, 0)$ on the $x$-axis. A point $F(5,15)$ is also given. Determine an expression for the sum of the areas of $\triangle DOE$ and $\triangle EOF$ in terms of $p$. Ensure your answer is simplified as much as possible.

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