
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
Two identical resistors, each with resistance \(R\), are connected in series and connected to a DC voltage source \(U\). An ideal voltmeter is connected in parallel to one of the resistors. Its reading is \(U_{v} = 10 \, V\). After that, the voltmeter is replaced with an ideal ammeter. The ammeter reading is \(I_{A} = 10 \, A\). Determine the value of \(R\).

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