
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 a triangle $\triangle ABC$ with internal angles $A$, $B$, $C$, and corresponding sides $a$, $b$, $c$. Also, $\sin(A-\frac{\pi}{4})=\frac{\sqrt{2}}{10}$.

1. Find the value of $\tan A$.
2. If the area of $\triangle ABC$ is $s=24$, and $b=10$, find the value of $a$.

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