
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
A discrete random variable \(X\) has a probability distribution given by:

| \(X\) | 3 | 4 | 5 | 6 | 7 |
| :--- | :--- | :--- | :--- | :--- | :--- |
| \(P\) | \(p_{1}\) | 0.15 | \(p_{3}\) | 0.25 | 0.35 |

Find the probabilities \(p_{1} = P(X=3)\) and \(p_{3} = P(X=5)\) given that \(p_{3}\) is 4 times \(p_{1}\).

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