
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 line $l$ passes through the point $(1,2)$ and its intercepts on the $x$-axis and $y$-axis are equal.

$(1)$ Find the general equation of line $l$;

$(2)$ If the intercepts of line $l$ on the $x$-axis and $y$-axis are not $0$, and point $P(a,b)$ is on line $l$, find the minimum value of $3^a + 3^b$.

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