
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
Let there be two isosceles triangles, $T$ and $T'$, which are not congruent but share the same perimeter. The sides of $T$ are of lengths $7$, $7$, and $10$. If the sides of $T'$ are $c$, $c$, and $d$, where $c \neq d$ and the perimeter of $T'$ is $24$, determine the value of $d$.

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