
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 triangle $ABC$, $A(0,1)$, the equation of the line containing the altitude $CD$ from $AB$ is $x+2y-4=0$, and the equation of the line containing the median $BE$ from $AC$ is $2x+y-3=0$.
1. Find the equation of line $AB$;
2. Find the equation of line $BC$;
3. Find the area of $\triangle BDE$.

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