
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 a geometric sequence with five terms \(t_{1}, t_{2}, t_{3}, t_{4}, t_{5}\), each term is positive and \(t_{1} > t_{2}\). If the sum of the first two terms is \(\frac{15}{2}\) and the sum of the squares of the first two terms is \(\frac{153}{4}\), what is the value of \(t_{5}\)?

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