
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
Given that the sum of the first $n$ terms of the arithmetic sequence $\{a_n\}$ is $S_n$, and the sum of the first $n$ terms of the geometric sequence $\{b_n\}$ is $T_n$. If $a_3=b_3$, $a_4=b_4$, and $\frac{S_5-S_3}{T_4-T_2}=5$, calculate the value of $\frac{a_5+a_3}{b_5+b_3}$.

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