
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
For what values of the velocity  $c$  does the equation  $u_t = u -u^2 + u_{xx}$  have a solution in the form of a traveling wave  $u = \varphi(x-ct)$ ,  $\varphi(-\infty) = 1$ ,  $\varphi(\infty) = 0$ ,  $0 \le u \le 1$ ?

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