\( \mid \leftarrow \quad \) Write (in the same base) the counting numbers just before and just after the given number. (Do not convert to base ten:) \[ 13_{\text {four }} \] The base-four counting number just before \( 13_{\text {four }} \) is \( \square \) four.

We need to find the number immediately before \( 13_{\text{four}} \) in base four. In base four, subtracting 1 works just like in base ten, but with digits \( 0, 1, 2, 3 \). Since \[ 13_{\text{four}} = 1 \times 4^1 + 3 \times 4^0, \] to subtract 1, we focus on the last digit: \[ 3 - 1 = 2. \] So, the digit in the ones place becomes \( 2 \) and the digit in the fours place remains \( 1 \). This gives: \[ 13_{\text{four}} - 1 = 12_{\text{four}}. \] Thus, the base-four counting number just before \( 13_{\text{four}} \) is \( 12_{\text{four}} \).