
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
Define a new operation of exponentiation: $x^{a}\oplus x^{b}=x^{ab}+x^{a+b}$. Solve the following problems using this operation rule.<br/>
$(1)$ Find the value of $2^{2}\oplus 2^{3}$;<br/>
$(2)$ If $2^{p}=3$, $2^{q}=5$, and $3^{q}=6$, find the value of $2^{p}\oplus 2^{q}$;<br/>
$(3)$ If the result of the operation $9\oplus 3^{2t}$ is $810$, what is the value of $t$?

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