
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
A copper wire with cross-sectional area $A$ carries a current $I$ during a short circuit. Initially, the wire's temperature was $T_{0}$. Estimate how long it will take for the wire to melt. Ignore radiation losses. The resistivity of the material depends on temperature: $\varrho=\varrho_{0}\left[1+\alpha\left(T-T_{0}\right)\right]$, where $\varrho_{0}$ is the resistivity at temperature $T_{0}$ and $\alpha$ is the temperature coefficient of the material. The temperature $T$ is given in Kelvin. Data: $\alpha=\frac{1}{235} \ {}^{\circ} \mathrm{C}^{-1}$, $\varrho_{0}=1.65 \cdot 10^{-8} \Omega \mathrm{m}$, $A=2 \mathrm{~mm}^{2}$, $I=120 \mathrm{~A}$, $T_{0}=313 \mathrm{~K}$.

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