
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
Solve the Dirichlet boundary value problem for the Helmholtz equation in a circle:

$$
\begin{gathered}
\Delta u + 4u = 0, \quad 0 \leq r < 1, \\
u|_{r=1} = \sin^3(\varphi).
\end{gathered}
$$

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