
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
Let $\{a_n\}$ be an arithmetic sequence, and $\{b_n\}$ be a geometric sequence, with $a_1=b_1=1$, $a_2+a_4=b_3$, and $b_2b_4=a_3$. Find the sum of the first 10 terms of $\{a_n\}$ and $\{b_n\}$, denoted as $S_{10}$ and $T_{10}$, respectively.

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