
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 $\triangle ABC$, $a$, $b$, and $c$ are the sides opposite to $\angle A$, $\angle B$, and $\angle C$ respectively, and $ac + c^2 = b^2 - a^2$. If the longest side of $\triangle ABC$ is $\sqrt{7}$ and $\sin C = 2\sin A$, find the length of the shortest side of $\triangle ABC$.

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